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On the Singularity of the Vlasov-Poisson System

Description: The Vlasov-Poisson system can be viewed as the collisionless limit of the corresponding Fokker- Planck-Poisson system. It is reasonable to expect that the result of Landau damping can also be obtained from the Fokker-Planck-Poisson system when the collision frequency v#23; approaches zero. However, we show that the colllisionless Vlasov-Poisson system is a singular limit of the collisional Fokker-Planck-Poisson system, and Landau's result can be recovered only as the #23; approaching zero from the positive side.
Date: April 26, 2013
Creator: and Hong Qin, Jian Zheng
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Partner: UNT Libraries Government Documents Department

Calculated thermal conductivities of pure gases and gaseous mixtures at elevated temperatures

Description: From summary: "A method of calculating thermal conductivities of gases and mixtures of gases at elevated temperatures is presented. Results for carbon dioxide, helium, neon, nitrogen, and their binary mixtures are given for the temperature range of 273 degrees Kelvin to 800 degrees Kelvin. The calculated results for the pure gases are in agreement with the known experimental data."
Date: 1951
Creator: Wright, J. M.
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A Class Of Generalized Kapchinskij-Vladimirskij Solutions And Associated Envelope Equations For High-intensity Charged Particle Beams

Description: A class of generalized Kapchinskij-Vladimirskij solutions of the nonlinear Vlasov-Maxwell equations and the associated envelope equations for high-intensity beams in a periodic lattice is derived. It includes the classical Kapchinskij-Vladimirskij solution as a special case. For a given lattice, the distribution functions and the envelope equations are specified by eight free parameters. The class of solutions derived captures a wider range of dynamical envelope behavior for high-intensity beams, and thus provides a new theoretical tool to investigate the dynamics of high-intensity beams.
Date: April 25, 2012
Creator: Qin, Hong & Davidson, Ronald C.
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Response to Comment on "On Higher-Order Corrections to Gyrokinetic Vlasov-Poisson Equations in the Long Wavelength Limit [Phys. Plasmas 16, 044506 (2009)]"

Description: We show in this Response that the nonlinear Poisson's equation in our original paper derived from the drift kinetic approach can be verified by using the nonlinear gyrokinetic Poisson's equation of Dubin et al. [Phys. Fluids 26, 3524 (1983)]. This nonlinear contribution in φ2 is indeed of the order of k4⊥ in the long wavelength limit and remains finite for zero ion temperature, in contrast to the nonlinear term by Parra and Catto [Plasma Phys. Control. Fusion 50, 065014 (2008)], which is of the order of k2⊥ and diverges for Ti → 0. For comparison, the leading term for the gyrokinetic Poisson's equation in this limit is of the order of k2⊥φ,
Date: November 20, 2009
Creator: Lee, W. W. & Kolensnikov, R. A.
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Kinetic Description of Intense Beam Propagation Through a Periodic Focusing Field for Uniform Phase-Space Density

Description: The Vlasov-Maxwell equations are used to investigate the nonlinear evolution of an intense sheet beam with distribution function f{sub b}(x,x{prime},s) propagating through a periodic focusing lattice k{sub x}(s+S) = k{sub x}(s), where S = const is the lattice period. The analysis considers the special class of distribution functions with uniform phase-space density f{sub b}(x,x{prime},s) = A = const inside of the simply connected boundary curves, x{prime}{sub +}(x,s) and x{prime}{sub -}(x,s), in the two-dimensional phase space (x,x{prime}). Coupled nonlinear equations are derived describing the self-consistent evolution of the boundary curves, x{prime}{sub +}(x,s) and x{prime}{sub -}(x,s), and the self-field potential {psi}(x,s) = e{sub b}{phi}(x,s)/{gamma}{sub b}m{sub b}{beta}{sub g}{sup 2}c{sup 2}. The resulting model is shown to be exactly equivalent to a (truncated) warm-fluid description with zero heat flow and triple-adiabatic equation-of-state with scalar pressure P{sub b}(x,s) = const x [n{sub b}(x,s)]. Such a fluid model is amenable to direct analysis by transforming to Lagrangian variables following the motion of a fluid element. Specific examples of periodically focused beam equilibria are presented, ranging from a finite-emittance beam in which the boundary curves in phase space (x,x{prime}) correspond to a pulsating parallelogram, to a cold beam in which the number density of beam particles, n{sub b}(x,s), exhibits large-amplitude periodic oscillations. For the case of a sheet beam with uniform phase-space density, the present analysis clearly demonstrates the existence of periodically focused beam equilibria without the undesirable feature of an inverted population in phase space that is characteristic of the Kapchinskij-Vladimirskij beam distribution.
Date: February 26, 2003
Creator: Davidson, Ronald C.; Qin, Hong; Tzenov, Stephan I. & Startsev, Edward A.
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Self-Consistent System of Equations for a Kinetic Description of the Low-Pressure Discharges Accounting for the Nonlocal and Collisionless Electron Dynamics

Description: In low-pressure discharges, when the electron mean free path is larger or comparable with the discharge length, the electron dynamics is essentially non-local. Moreover, the electron energy distribution function (EEDF) deviates considerably from a Maxwellian. Therefore, an accurate kinetic description of the low-pressure discharges requires knowledge of the non-local conductivity operator and calculation of the non-Maxwellian EEDF. The previous treatments made use of simplifying assumptions: a uniform density profile and a Maxwellian EEDF. In the present study a self-consistent system of equations for the kinetic description of nonlocal, non-uniform, nearly collisionless plasmas of low-pressure discharges is derived. It consists of the nonlocal conductivity operator and the averaged kinetic equation for calculation of the non-Maxwellian EEDF. The importance of accounting for the non-uniform plasma density profile on both the current density profile and the EEDF is demonstrated.
Date: May 19, 2003
Creator: Kaganovich, Igor D. & Polomarov, Oleg
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Partner: UNT Libraries Government Documents Department

The Hamiltonian Structure and Euler-Poincare Formulation of the Valsov-Maxwell and Gyrokinetic System

Description: We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function. Using a Legendre transform, we explicitly derive the field theoretic Hamiltonian structure of the system. This is carried out with the Dirac theory of constraints, which is used to construct meaningful brackets from those obtained directly from Euler-Poincare theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models and Casimir type stability methods. __________________________________________________
Date: September 25, 2012
Creator: Squire, J.; Qin, H. & Tang, W. M.
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Combined Ideal and Kinetic Effects on Reversed Shear Alfven Eigenmodes

Description: A theory of Reversed Shear Alfven Eigenmodes (RSAEs) is developed for reversed magnetic field shear plasmas when the safety factor minimum, qmin, is at or above a rational value. The modes we study are known sometimes as either the bottom of the frequency sweep or the down sweeping RSAEs. We show that the ideal MHD theory is not compatible with the eigenmode solution in the reversed shear plasma with qmin above integer values. Corrected by special analytic FLR condition MHD dispersion of these modes nevertheless can be developed. Large radial scale part of the analytic RSAE solution can be obtained from ideal MHD and expressed in terms of the Legendre functions. The kinetic equation with FLR effects for the eigenmode is solved numerically and agrees with the analytic solutions. Properties of RSAEs and their potential implications for plasma diagnostics are discussed.
Date: May 23, 2011
Creator: N.N. Gorelenkov, G.J. Kramer, and R. Nazikian
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Partner: UNT Libraries Government Documents Department

Physics of Substorm Growth Phase, Onset, and Dipolarization

Description: A new scenario of substorm growth phase, onset, and depolarization during expansion phase and the corresponding physical processes are presented. During the growth phase, as a result of enhanced plasma convection, the plasma pressure and its gradient are continued to be enhanced over the quiet-time values in the plasma sheet. Toward the late growth phase, a strong cross-tail current sheet is formed in the near-Earth plasma sheet region, where a local magnetic well is formed, the plasma beta can reach a local maximum with value larger than 50 and the cross-tail current density can be enhanced to over 10nA/m{sup 2} as obtained from 3D quasi-static magnetospheric equilibrium solutions for the growth phase. The most unstable kinetic ballooning instabilities (KBI) are expected to be located in the tailward side of the strong cross-tail current sheet region. The field lines in the most unstable KBI region map to the transition region between the region-1 and region-2 currents in the ionosphere, which is consistent with the observed initial brightening location of the breakup arc in the intense proton precipitation region. The KBI explains the AMPTE/CCE observations that a low-frequency instability with a wave period of 50-75 seconds is excited about 2-3 minutes prior to substorm onset and grows exponentially to a large amplitude at the onset of current disruption (or current reduction). At the current disruption onset higher frequency instabilities are excited so that the plasma and electromagnetic field fluctuations form a strong turbulent state. Plasma transport takes place due to the strong turbulence to relax the ambient plasma pressure profile so that the plasma pressure and current density are reduced and the ambient magnetic field intensity increases by more than a factor of 2 in the high-beta(sub)eq region and the field line geometry recovers from tail-like to dipole-like dipolarization.
Date: October 22, 2003
Creator: Cheng, C.Z.
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Partner: UNT Libraries Government Documents Department

Landau Damping and Anomalous Skin Effect in Low-pressure Gas Discharges: Self-consistent Treatment of Collisionless Heating

Description: In low-pressure discharges, where the electron mean free path is larger or comparable with the discharge length, the electron dynamics is essentially nonlocal. Moreover, the electron energy distribution function (EEDF) deviates considerably from a Maxwellian. Therefore, an accurate kinetic description of the low-pressure discharges requires knowledge of the nonlocal conductivity operator and calculation of the non-Maxwellian EEDF. The previous treatments made use of simplifying assumptions: a uniform density profile and a Maxwellian EEDF. In the present study a self-consistent system of equations for the kinetic description of nonlocal, nonuniform, nearly collisionless plasmas of low-pressure discharges is reported. It consists of the nonlocal conductivity operator and the averaged kinetic equation for calculation of the non-Maxwellian EEDF. This system was applied to the calculation of collisionless heating in capacitively and inductively coupled plasmas. In particular, the importance of accounting for the nonuniform plasma density profile for computing the current density profile and the EEDF is demonstrated. The enhancement of collisionless heating due to the bounce resonance between the electron motion in the potential well and the external radio-frequency electric field is investigated. It is shown that a nonlinear and self-consistent treatment is necessary for the correct description of collisionless heating.
Date: January 30, 2004
Creator: Kaganovich, Igor D.; Polomarov, Oleg V. & Theodosiou, Constantine E.
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Partner: UNT Libraries Government Documents Department

Modeling of ICRH H-minority-driven n = 1 Resonant Modes in JET

Description: A nonperturbative code NOVA-KN (Kinetic Nonperturbative) has been developed to account for finite orbit width (FOW) effects in nonperturbative resonant modes such as the low-frequency MHD modes observed in the Joint European Torus (JET). The NOVA-KN code was used to show that the resonant modes with frequencies in the observed frequency range are ones having the characteristic toroidal precession frequency of H-minority ions. Results are similar to previous theoretical studies of fishbone instabilities, which were found to exist at characteristic precession frequencies of hot ions.
Date: August 21, 2003
Creator: Gorelenkov, N.N.; Mantsinen, M.J.; Sharapov, S.E.; Cheng, C.Z. & Contributors, the JET-EFDA
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Partner: UNT Libraries Government Documents Department

Particle-in-cell Simulations with Kinetic Electrons

Description: A new scheme, based on an exact separation between adiabatic and nonadiabatic electron responses, for particle-in-cell (PIC) simulations of drift-type modes is presented. The (linear and nonlinear) elliptic equations for the scalar fields are solved using a multi-grid solver. The new scheme yields linear growth rates in excellent agreement with theory and it is shown to conserve energy well into the nonlinear regime. It is also demonstrated that simulations with few electrons are reliable and accurate, suggesting that large-scale, PIC simulations with electron dynamics in toroidal geometry (e.g., tokamaks and stellarators plasmas) are within reach of present-day massively parallel supercomputers.
Date: February 12, 2004
Creator: Lewandowski, J.L.V.
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A turbulence model for buoyant flows based on vorticity generation.

Description: A turbulence model for buoyant flows has been developed in the context of a k-{var_epsilon} turbulence modeling approach. A production term is added to the turbulent kinetic energy equation based on dimensional reasoning using an appropriate time scale for buoyancy-induced turbulence taken from the vorticity conservation equation. The resulting turbulence model is calibrated against far field helium-air spread rate data, and validated with near source, strongly buoyant helium plume data sets. This model is more numerically stable and gives better predictions over a much broader range of mesh densities than the standard k-{var_epsilon} model for these strongly buoyant flows.
Date: October 1, 2005
Creator: Domino, Stefan Paul; Nicolette, Vernon F.; O'Hern, Timothy John; Tieszen, Sheldon R. & Black, Amalia Rebecca
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Partner: UNT Libraries Government Documents Department

Truncated Thermal Equilibrium Distribution for Intense Beam Propagation

Description: An intense charged-particle beam with directed kinetic energy ({lambda}{sub b}-1)m{sub b}c{sup 2} propagates in the z-direction through an applied focusing field with transverse focusing force modeled by F{sub foc} = -{lambda}{sub b}m{sub b}{omega}{sub beta}{sup 2} {perpendicular} x {perpendicular} in the smooth focusing approximation. This paper examines properties of the axisymmetric, truncated thermal equilibrium distribution F(sub)b(r,p perpendicular) = A exp (-H Perpendicular/T perpendicular (sub)b) = (H perpendicular-E(sub)b), where A, T perpendicular (sub)b, and E (sub)b are positive constants, and H perpendicular is the Hamiltonian for transverse particle motion. The equilibrium profiles for beam number density, n(sub)b(r) = * d{sup 2}pF(sub)b(r,p perpendicular), and transverse temperature, T perpendicular (sub)b(r) = * d{sup 2}p(p{sup 2} perpendicular/2 lambda (sbu)bm (sub)b)F(sub)b(r,p perpendicular), are calculated self-consistently including space-charge effects. Several properties of the equilibrium profiles are noteworthy. For example, the beam has a sharp outer edge radius r(sub)b with n(sub)b(r greater than or equal to rb) = 0, where r(sub)b depends on the value of E(sub)b/T (sub)perpendicular(sub)b. In addition, unlike the choice of a semi-Gaussian distribution, F{sup SG}(sub)b = A exp (-p{sup 2}(sub)perpendicular/2lambda(sub)bm(sub)bTperpendicular(sub)b) = (r-r(sub)b), the truncated thermal equilibrium distribution F(sub)b(r,p) depends on (r,p) only through the single-particle constant of the motion Hperpendiuclar and is therefore a true steady-state solution (*/*t = 0) of the nonlinear Vlasov-Maxwell equations.
Date: February 26, 2003
Creator: Davidson, Ronald C.; Qin, Hong & Lund, Steven M.
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Partner: UNT Libraries Government Documents Department

Introduction to Gyrokinetic Theory with Applications in Magnetic Confinement Research in Plasma Physics

Description: The present lecture provides an introduction to the subject of gyrokinetic theory with applications in the area of magnetic confinement research in plasma physics--the research arena from which this formalism was originally developed. It was presented as a component of the ''Short Course in Kinetic Theory within the Thematic Program in Partial Differential Equations'' held at the Fields Institute for Research in Mathematical Science (24 March 2004). This lecture also discusses the connection between the gyrokinetic formalism and powerful modern numerical simulations. Indeed, simulation, which provides a natural bridge between theory and experiment, is an essential modern tool for understanding complex plasma behavior. Progress has been stimulated in particular by the exponential growth of computer speed along with significant improvements in computer technology. The advances in both particle and fluid simulations of fine-scale turbulence and large-scale dynamics have produced increasingly good agreement between experimental observations and computational modeling. This was enabled by two key factors: (i) innovative advances in analytic and computational methods for developing reduced descriptions of physics phenomena spanning widely disparate temporal and spatial scales and (ii) access to powerful new computational resources.
Date: January 3, 2005
Creator: Tang, W.M.
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Fusion Reaction Rate in an Inhomogeneous Plasma

Description: The local fusion rate, obtained from the assumption that the distribution is a local Maxwellian, is inaccurate if mean-free-paths of fusing particles are not sufficiently small compared with the inhomogeneity length of the plasma. We calculate the first order correction of P0 in terms of the small spatial gradient and obtain a non-local modification of P(sub)0 in a shock region when the gradient is not small. Use is made of the fact that the fusion reaction cross section has a relatively sharp peak as a function of energy.
Date: September 3, 2004
Creator: Son, S. & Fisch, N.J.
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Pullback Transformations in Gyrokinetic Theory

Description: The Pullback transformation of the distribution function is a key component of the gyrokinetic theory. In this paper, a systematic treatment of this subject is presented, and results from applications of the uniform framework developed are reviewed. The focus is on providing a clear exposition of the basic formalism which arises from the existence of three distinct coordinate systems in gyrokinetic theory. The familiar gyrocenter coordinate system, where the gyromotion is decoupled from the rest of particle's dynamics, is non-canonical and non-fabric. On the other hand, Maxwell's equations, which are needed to complete a kinetic system, are initially only defined in the fabric laboratory phase space coordinate system. The pullback transformations provide a rigorous connection between the distribution functions in gyrocenter coordinates and Maxwell's equations in laboratory phase space coordinates. This involves the generalization of the usual moment integrals originally defined on the cotangent fiber of the phase space to the moment integrals on a general 6D symplectic manifold, is shown to be an important step in the proper formulation of gyrokinetic theory. The resultant systematic treatment of the moment integrals enabled by the pullback transformation. Without this vital element, a number of prominent physics features, such as the presence of the compressional Alfven wave and a proper description of the gyrokinetic equilibrium, cannot be readily recovered.
Date: January 21, 2003
Creator: Qin, H. & Tang, W.M.
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Partner: UNT Libraries Government Documents Department