Volpe<i>et al.</i>Reply:

Volpe, Giovanni; Helden, Laurent; Brettschneider, Thomas; Wehr, Jan; Bechinger, Clemens

doi:10.1103/physrevlett.107.078902

Cited by 20 publications

(26 citation statements)

References 5 publications

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“…Theoretical calculations in the early 1980's showed the feasibility of using rf current drive to stabilize tearing modes [3,4]. The recognition in the late 1990's that bootstrap currents were driving NTMs in hot, collisionless tokamak plasmas [5][6][7][8], led to a resurgence of theoretical work in this area [9][10][11][12][13], to experimental demonstrations of stabilization [14][15][16][17][18][19][20], and to continuing intensive attention [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. A variety of rf waves are used to drive current [41], but, for stabilizing the NTM, the most studied methods are electron cyclotron current drive (ECCD) [42] and lower hybrid current drive (LHCD) [43].…”

Section: Pacs Numbersmentioning

confidence: 99%

Suppression of Tearing Modes by Radio Frequency Current Condensation

Reiman

Fisch

2018

Phys. Rev. Lett.

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Currents driven by rf (radio frequency) waves in the interior of magnetic islands can stabilize deleterious tearing modes in tokamaks. Present analyses of stabilization assume that the local electron acceleration is unaffected by the presence of the island. However, the power deposition and electron acceleration are sensitive to the perturbation of the temperature. The nonlinear feedback on the power deposition in the island increases the temperature perturbation, and can lead to a bifurcation of the solution to the steady-state heat diffusion equation. The combination of the nonlinearly enhanced temperature perturbation with the rf current drive sensitivity to the temperature leads to an rf current condensation effect, which can increase the efficiency of rf current drive stabilization and reduce its sensitivity to radial misalignment of the ray trajectories. The threshold for the effect is in a regime that has been encountered in experiments, and will likely be encountered in ITER. PACS numbers:Introduction: A study of the root causes of disruptions in the JET tokamak found that neoclassical tearing modes (NTMs) were the single most common cause [1,2]. Theoretical calculations in the early 1980's showed the feasibility of using rf current drive to stabilize tearing modes [3,4]. The recognition in the late 1990's that bootstrap currents were driving NTMs in hot, collisionless tokamak plasmas [5][6][7][8], led to a resurgence of theoretical work in this area [9][10][11][12][13], to experimental demonstrations of stabilization [14][15][16][17][18][19][20], and to continuing intensive attention [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. A variety of rf waves are used to drive current [41], but, for stabilizing the NTM, the most studied methods are electron cyclotron current drive (ECCD) [42] and lower hybrid current drive (LHCD) [43]. ITER is designed with an NTM ECCD stabilization capability, with continued effort to model and improve this capability [25,29,30,44]. We identify here an rf current condensation effect, previously overlooked, which can significantly facilitate island stabilization.Calculations of rf stabilization of magnetic islands assume, at present, that the local acceleration of electrons is unaffected by the presence of the island. However, the local deposition is sensitive to small changes in the temperature, and these changes can be significantly affected by the presence of an island. The effect on the local deposition becomes significant when the fractional temperature perturbation exceeds about 5% for electron cyclotron waves and 2.5% for lower hybrid waves. Temperature perturbations as high as 20% have been measured in islands in rf stabilization experiments [45].In the conventional picture of rf current drive stabilization of a rotating island, a geometric effect associated with the equilibration of the rf driven current density within the flux surfaces of the island leads to a higher current density near the center of the island than near its peripher...

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Section: Pacs Numbersmentioning

confidence: 99%

Suppression of Tearing Modes by Radio Frequency Current Condensation

Reiman

Fisch

2018

Phys. Rev. Lett.

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“…Its explicit form is now much harder to derive than in the case of the minimal model of section 2. In the case discussed in section 3.1, it is possible (but not necessary) to interpret it in terms of a stochastic integration convention choice (α = 1) [28,29], as explained in section 2, but no such interpretation is possible in the generality of the examples considered in section 3.…”

Section: A Minimal Discrete-time Modelmentioning

confidence: 99%

“…noise induced drift (29) The outline of the derivation is provided in appendix D. The second term has the same structure as the noise-induced drift in the Brownian motion case: it is proportional to the product of the original noise coefficient, ( ) σF x , and its spatial derivative (see section 3.1). The proportionality constant depends on the time scales of the problem as [22].…”

Section: Delayed Multiplicative Feedback and Colored Noisementioning

confidence: 99%

“…which agrees well with the experimental results, as shown in figure 11; see also [90] where a more precise calculation yields α = − δ τ e 1 2 . SDE (29) is written here in the Itô form, but it can be interpreted according to another convention, corresponding to another choice of the parameter α, as described in section 2. In this language, the presence of such delay made the SDE describing the behavior of the electric circuit with multiplicative noise cross over from obeying the Stratonovich convention (α = 0.5) to obeying the Itô convention (α = 0), as the ratio between the colored noise correlation time τ and the feedback delay δ varied (equation (30)), as shown in figures 10(b)-(e).…”

Section: Delayed Multiplicative Feedback and Colored Noisementioning

confidence: 99%

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Effective drifts in dynamical systems with multiplicative noise: a review of recent progress

2016

Self Cite

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Noisy dynamical models are employed to describe a wide range of phenomena. Since exact modeling of these phenomena requires access to their microscopic dynamics, whose time scales are typically much shorter than the observable time scales, there is often need to resort to effective mathematical models such as stochastic differential equations (SDEs). In particular, here we consider effective SDEs describing the behavior of systems in the limits when natural time scales become very small. In the presence of multiplicative noise (i.e. noise whose intensity depends upon the system's state), an additional drift term, called noise-induced drift or effective drift, appears. The nature of this noise-induced drift has been recently the subject of a growing number of theoretical and experimental studies. Here, we provide an extensive review of the state of the art in this field. After an introduction, we discuss a minimal model of how multiplicative noise affects the evolution of a system. Next, we consider several case studies with a focus on recent experiments: the Brownian motion of a microscopic particle in thermal equilibrium with a heat bath in the presence of a diffusion gradient; the limiting behavior of a system driven by a colored noise modulated by a multiplicative feedback; and the behavior of an autonomous agent subject to sensorial delay in a noisy environment. This allows us to present the experimental results, as well as mathematical methods and numerical techniques, that can be employed to study a wide range of systems. At the end we give an application-oriented overview of future projects involving noise-induced drifts, including both theory and experiment.

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“…As counter-intuitive as this may seem, some experiments [34,35] have nonetheless claimed to have found empirical evidence that there could indeed be physical systems where α = 1. We now focus on a discussion of [34,35], noting that [34] has been the subject of a comment [36] and a reply [37]: we will show that some of the arguments in [34] are not well-founded.…”

Section: A Recent Case Study: Anticipating Sde'smentioning

confidence: 99%

Itô Versus Stratonovich: 30 Years Later

Mannella

McClintock

2012

Fluct. Noise Lett.

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The Itô versus Stratonovich controversy, about the "correct" calculus to use for integration of Langevin equations, was settled to general satisfaction some 30 years ago. Recently, however, it has started to re-emerge, following the advent of new experimental techniques. We briefly review the historical background and discuss critically some of the most recent contributions. We show that some of the new findings are not well based.

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Volpeet al.Reply:

Cited by 20 publications

References 5 publications

Suppression of Tearing Modes by Radio Frequency Current Condensation

Suppression of Tearing Modes by Radio Frequency Current Condensation

Effective drifts in dynamical systems with multiplicative noise: a review of recent progress

Itô Versus Stratonovich: 30 Years Later

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