scholarly journals TEST PARTICLE SIMULATIONS FOR NON-MAXWELLIAN PLASMA TRANSPORT: DISCRETIZED COLLISIONAL OPERATOR

2021 ◽  
pp. 31-35
Author(s):  
D.V. Vozniuk ◽  
O.A. Shyshkin ◽  
I.O. Girka
Keyword(s):  
Distribution Function ◽  
Test Particle ◽  
Plasma Heating ◽  
Equivalent Form ◽  
Collision Operator ◽  
Maxwellian Distribution ◽  
Direct Result ◽  
Coulomb Collisions ◽  
Toroidal Plasma ◽  
Maxwellian Plasma

The plasma observed in modern fusion devices is very often characterized by strongly non Maxwellian distribution function. That is the direct result of inevitable application of plasma heating techniques, such as neutral beam injection (NBI) and ion/electron cyclotron resonance frequency (ICRF/ECRF) heating, which induce the non Maxwellian fast ions. Another cause of transfer from Maxwellian to non Maxwellian is the reconnection of magnetic field lines followed by formation of magnetic resonant structures like magnetic islands and stochastic layers. One of the basic approaches used to simulate fusion plasma is test particle approach based on a solution of the equations of test particle motion. To make this approach more comprehensive one should take care of plasma particle interactions, i.e. Coulomb collisions in non Maxwellian environment. In present paper the expressions for the discretized collision operator of a general Monte Carlo equivalent form in terms of expectation values and standard deviation for an arbitrary non Maxwellian bulk distribution function are derived. The modification of transport coefficients of impurity ions caused by the transition from the background Maxwellian to non Maxwellian plasma is studied by means of this discretized collision operator. On this purpose, the set of monoenergetic neon test impurities is followed in a toroidal plasma consisting of bulk deuterons and electrons. The non Maxwellian distribution of the bulk is obtained by adding a fraction of energetic particles of the same species. It is demonstrated that a change of collision frequencies of impurities takes place in presence of this energetic fraction leading to a change of impurity neoclassical transport regime.

scholarly journals Landau Modes are Eigenmodes of Stellar Systems in the Limit of Zero Collisions

2021 ◽  
Vol 923 (2) ◽  
pp. 271
Author(s):  
C. S. Ng ◽  
A. Bhattacharjee
Keyword(s):  
Distribution Function ◽  
Unstable Mode ◽  
Stellar System ◽  
Collision Operator ◽  
Thermal Fluctuations ◽  
Maxwellian Distribution ◽  
Gravitational Forces ◽  
Gravitational Systems ◽  
Maxwellian Distribution Function ◽  
Spectrum Of Eigenmodes

Abstract We consider the spectrum of eigenmodes in a stellar system dominated by gravitational forces in the limit of zero collisions. We show analytically and numerically using the Lenard–Bernstein collision operator that the Landau modes, which are not true eigenmodes in a strictly collisionless system (except for the Jeans unstable mode), become part of the true eigenmode spectrum in the limit of zero collisions. Under these conditions, the continuous spectrum of true eigenmodes in a collisionless system, also known as the Case–van Kampen modes, is eliminated. Furthermore, because the background distribution function in a weakly collisional system can exhibit significant deviations from a Maxwellian distribution function over long times, we show that the spectrum of Landau modes can change drastically even in the presence of slight deviations from a Maxwellian, primarily through the appearance of weakly damped modes that may be otherwise heavily damped for a Maxwellian distribution. Our results provide important insights for developing statistical theories to describe thermal fluctuations in a stellar system, which are currently a subject of great interest for N-body simulations as well as observations of gravitational systems.

Averaged collision strength of Carbon Π ion of Druyvesteyn distribution in plasma

2018 ◽  
Vol 32 (26) ◽  
pp. 1850316 ◽  
Author(s):  
Jian He ◽  
Qingguo Zhang
Keyword(s):  
Space Plasma ◽  
Maxwellian Distribution ◽  
Collision Strength ◽  
Maxwellian Plasma ◽  
Increasing Temperature

Non-Maxwellian distribution has been found in laboratory and space plasma in recent years. In this paper, averaged collision strengths of Carbon [Formula: see text] ion 133.53 nm are calculated for Druyvesteyn distribution for the non-Maxwellian distribution, when temperatures vary from 10[Formula: see text] K to 10[Formula: see text] K. Results indicate that significant differences between the averaged collision strengths occur for the Druyvesteyn distribution and the Maxwellian distribution, furthermore, for the Maxwellian distribution and the Druyvesteyn distribution with any characterizing parameter x, the averaged collision strengths increase with increasing temperature, and the averaged collision strengths are close to those of the Maxwellian distribution when the characterizing parameter x is close to [Formula: see text]. This calculation is significant for non-Maxwellian plasma.

scholarly journals Projection-operator methods for classical transport in magnetized plasmas. Part 1. Linear response, the Braginskii equations and fluctuating hydrodynamics

2018 ◽  
Vol 84 (4) ◽  
Author(s):  
John A. Krommes
Keyword(s):  
Distribution Function ◽  
Projection Operator ◽  
Linear Response ◽  
Transport Coefficients ◽  
Collision Operator ◽  
Transport Equations ◽  
Transport Processes ◽  
Projection Operators ◽  
Covariant Representation ◽  
Classical Transport

An introduction to the use of projection-operator methods for the derivation of classical fluid transport equations for weakly coupled, magnetised, multispecies plasmas is given. In the present work, linear response (small perturbations from an absolute Maxwellian) is addressed. In the Schrödinger representation, projection onto the hydrodynamic subspace leads to the conventional linearized Braginskii fluid equations when one restricts attention to fluxes of first order in the gradients, while the orthogonal projection leads to an alternative derivation of the Braginskii correction equations for the non-hydrodynamic part of the one-particle distribution function. The projection-operator approach provides an appealingly intuitive way of discussing the derivation of transport equations and interpreting the significance of the various parts of the perturbed distribution function; it is also technically more concise. A special case of the Weinhold metric is used to provide a covariant representation of the formalism; this allows a succinct demonstration of the Onsager symmetries for classical transport. The Heisenberg representation is used to derive a generalized Langevin system whose mean recovers the linearized Braginskii equations but that also includes fluctuating forces. Transport coefficients are simply related to the two-time correlation functions of those forces, and physical pictures of the various transport processes are naturally couched in terms of them. A number of appendices review the traditional Chapman–Enskog procedure; record some properties of the linearized Landau collision operator; discuss the covariant representation of the hydrodynamic projection; provide an example of the calculation of some transport effects; describe the decomposition of the stress tensor for magnetised plasma; introduce the linear eigenmodes of the Braginskii equations; and, with the aid of several examples, mention some caveats for the use of projection operators.

Bootstrap-current computations for a stellarator-reactor plasma

1990 ◽  
Vol 44 (3) ◽  
pp. 431-453 ◽  
Author(s):  
W. D. D'Haeseleer ◽  
W. N. G. Hitchon ◽  
C. D. Beidler ◽  
J. L. Shohet
Keyword(s):  
Distribution Function ◽  
Kinetic Equation ◽  
Physical Interpretation ◽  
Collision Operator ◽  
Numerical Code ◽  
Parallel Flows ◽  
Bootstrap Current ◽  
The Difference ◽  
Rotational Transform ◽  
The Impact

Numerical results for the bootstrap current in a stellarator-reactor plasma are presented. The distribution function f is computed numerically from a kinetic equation that is averaged over the helical ripple. The parallel flows and the current are obtained as v‖ moments of f. The physics issues embedded in the code are discussed concisely, concentrating on the justification as to why the bootstrap current can be estimated from an averaged scheme. Results are presented for typical stellarator-reactor parameters. The numerical code FLOCS predicts that the momentum-restoring terms in the collision operator have no significant impact on the value of the bootstrap current (the difference being about 10%). The results obtained are related to the equilibrium flows, and a physical interpretation based on the kinetic picture is presented. Finally, an estimate for the impact of J‖ on the rotational transform is given.

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