Smoluchowski Equation in Cumulant Approximation

Pereverzev, Yuriy V.; Pereverzev, Andrey; Prezhdo, Eugenia

doi:10.7566/jpsj.82.024001

Cited by 4 publications

(4 citation statements)

References 86 publications

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“…4(d) was obtained by the ASTRA simulation. 43 Figure 5 plots the density and pressure fractions of the fusion born a's, again obtained by ASTRA. These EPs occupy about 1% of the total fuel density at the plasma core, but contribute to about 20% of the thermal pressure close to the core.…”

Section: A Iter Equilibriamentioning

confidence: 99%

Non-perturbative modelling of energetic particle effects on resistive wall mode: Anisotropy and finite orbit width

et al. 2014

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A non-perturbative magnetohydrodynamic-kinetic hybrid formulation is developed and implemented into the MARS-K code [Liu et al., Phys. Plasmas 15, 112503 (2008)] that takes into account the anisotropy and asymmetry [Graves et al., Nature Commun. 3, 624 (2012)] of the equilibrium distribution of energetic particles (EPs) in particle pitch angle space, as well as first order finite orbit width (FOW) corrections for both passing and trapped EPs. Anisotropic models, which affect both the adiabatic and non-adiabatic drift kinetic energy contributions, are implemented for both neutral beam injection and ion cyclotron resonant heating induced EPs. The first order FOW correction does not contribute to the precessional drift resonance of trapped particles, but generally remains finite for the bounce and transit resonance contributions, as well as for the adiabatic contributions from asymmetrically distributed passing particles. Numerical results for a 9MA steady state ITER plasma suggest that (i) both the anisotropy and FOW effects can be important for the resistive wall mode stability in ITER plasmas; and (ii) the non-perturbative approach predicts less kinetic stabilization of the mode, than the perturbative approach, in the presence of anisotropy and FOW effects for the EPs. The latter may partially be related to the modification of the eigenfunction of the mode by the drift kinetic effects. [http://dx.

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Section: A Iter Equilibriamentioning

confidence: 99%

Non-perturbative modelling of energetic particle effects on resistive wall mode: Anisotropy and finite orbit width

et al. 2014

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“…As we have already stressed, the concept of generalized cumulants has been developed and applied in many dierent contexts of physics: dynamical mean-field theory [23], coupled bosons and valence electrons coupled to plasmons [24,25], multiple plasmons in photoemission [26], dynamic perturbations in metals [27], one-electron Green function [28], entanglement between electronic domains and reduced density matrix for coupled electrons in general [12][13][14][15][16][17][18][19], extending Wick theorem in particle physics [29][30][31] and in many fields of statistical mechanics [6,7,10,11,[20][21][22][32][33][34][35][36][37][38], just to quote some among many others.…”

Section: Kubo's Idea For Generalized Cumulants and The Related Criticismmentioning

confidence: 99%

About the foundation of the Kubo generalized cumulants theory: a revisited and corrected approach

Bianucci¹,

Bologna²

2020

J. Stat. Mech.

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More than fifty years ago, in a couple of seminal works (Kubo 1962 J. Phys. Soc. Japan 17 1100–20; Kubo 1963 J. Math. Phys. 4 174–83) Kubo introduced the important idea of generalized cumulants, extending to stochastic operators this concept implicitly introduced by Laplace in 1810. Kubo’s idea has been applied in several branches of physics, where the result of the average process is a Lioville operator or an effective time evolution operator for the density matrix of spin systems or the reduced density matrix for boson-fermions etc. Despite this success, the theoretical developments in these Kubo works pose problems that were highlighted many years ago by Fox and van Kampen and never solved. These weaknesses and errors, in particular concerning the factorization property of exponentials of cumulants and the explicit expressions that give generalized cumulants in terms of generalized moments and vice-versa, caused some perplexity (and confusion) about the possible application of this procedure, limiting its use, in practice. In the present paper, we give a sound ground to the approach to cumulant operators, working in a general framework that shows the potentiality of the old Kubo idea, today not yet fully exploited. It results that, for the same moment operators, different definitions of generalized cumulants can be adopted. A general Kubo–Meeron closed-form formula giving cumulant operators in terms of moment operators cannot be obtained, but the reverse one, cumulants in terms of operators, is given and, noticeably, formally it does not depend on the specific nature of the moments, but just on the definition of the generalized cumulants.

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“…As we have already stressed, the concept of generalized cumulants has been developed and applied in many different contexts of physics: dynamical mean-field theory 24 , coupled bosons and valence electrons coupled to plasmons 25,26 , multiple plasmons in photoemission 27 , dynamic perturbations in metals 28 , one-electron Green function 29 , entanglement between electronic domains and reduced density matrix for coupled electrons in general [12][13][14][15][16][17][18][19] , extending Wick theorem in particle physics [30][31][32] and in many field of statistical mechanics 6,7, 10,11,[21][22][23][33][34][35][36][37][38][39] , just to quote some among many others.…”

Section: The Kubo's Idea For Generalized Cumulants and The Related Cr...mentioning

confidence: 99%

About the foundation of the Kubo Generalized Cumulants theory. A revisited and corrected approach

Bianucci,

Bologna

2019

Preprint

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Smoluchowski Equation in Cumulant Approximation

Cited by 4 publications

References 86 publications

Non-perturbative modelling of energetic particle effects on resistive wall mode: Anisotropy and finite orbit width

Non-perturbative modelling of energetic particle effects on resistive wall mode: Anisotropy and finite orbit width

About the foundation of the Kubo generalized cumulants theory: a revisited and corrected approach

About the foundation of the Kubo Generalized Cumulants theory. A revisited and corrected approach

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