Showing papers in "Physics of Plasmas in 2002"

Ablation of solids by femtosecond lasers: ablation mechanism and ablation thresholds for metals and dielectrics

Abstract: The mechanism of ablation of solids by intense femtosecond laser pulses is described in an explicit analytical form. It is shown that at high intensities when the ionization of the target material is complete before the end of the pulse, the ablation mechanism is the same for both metals and dielectrics. The physics of this new ablation regime involves ion acceleration in the electrostatic field caused by charge separation created by energetic electrons escaping from the target. The formulas for ablation thresholds and ablation rates for metals and dielectrics, combining the laser and target parameters, are derived and compared to experimental data. The calculated dependence of the ablation thresholds on the pulse duration is in agreement with the experimental data in a femtosecond range, and it is linked to the dependence for nanosecond pulses.

Edge localized modes and the pedestal: A model based on coupled peeling–ballooning modes

Abstract: A model based on magnetohydrodynamic (MHD) stability of the tokamak plasma edge region is presented, which describes characteristics of edge localized modes (ELMs) and the pedestal. The model emphasizes the dual role played by large bootstrap currents driven by the sharp pressure gradients in the pedestal region. Pedestal currents reduce the edge magnetic shear, stabilizing high toroidal mode number (n) ballooning modes, while at the same time providing drive for intermediate to low n peeling modes. The result is that coupled peeling–ballooning modes at intermediate n (3

Electric field detection in laser-plasma interaction experiments via the proton imaging technique

Abstract: Due to their particular properties, the beams of the multi-MeV protons generated during the interaction of ultraintense (I>1019 W/cm2) short pulses with thin solid targets are most suited for use as a particle probe in laser-plasma experiments. The recently developed proton imaging technique employs the beams in a point-projection imaging scheme as a diagnostic tool for the detection of electric fields in laser-plasma interaction experiments. In recent investigations carried out at the Rutherford Appleton Laboratory (RAL, UK), a wide range of laser-plasma interaction conditions of relevance for inertial confinement fusion (ICF)/fast ignition has been explored. Among the results obtained will be discussed: the electric field distribution in laser-produced long-scale plasmas of ICF interest; the measurement of highly transient electric fields related to the generation and dynamics of hot electron currents following ultra-intense laser irradiation of targets; the observation in underdense plasmas, after the ...

Numerical studies of edge localized instabilities in tokamaks

Abstract: A new computational tool, edge localized instabilities in tokamaks equilibria (ELITE), has been developed to help our understanding of short wavelength instabilities close to the edge of tokamak plasmas. Such instabilities may be responsible for the edge localized modes observed in high confinement H-mode regimes, which are a serious concern for next step tokamaks because of the high transient power loads which they can impose on divertor target plates. ELITE uses physical insight gained from analytic studies of peeling and ballooning modes to provide an efficient way of calculating the edge ideal magnetohydrodynamic stability properties of tokamaks. This paper describes the theoretical formalism which forms the basis for the code.

Cylindrical and spherical dust ion–acoustic solitary waves

Abstract: The properties of cylindrical and spherical dust ion–acoustic solitary waves (DIASWs) in an unmagnetized dusty plasma, whose constituents are inertial ions, Boltzmann electrons, and stationary dust particles, are investigated by employing the reductive perturbation method. The modified Korteweg–de Vries equation is derived and its numerical solutions are obtained. It has been found that the properties of the DIASWs in a nonplanar cylindrical or spherical geometry differ from those in a planar one-dimensional geometry.

On the role of the purely transverse Weibel instability in fast ignitor scenarios

Abstract: The growth rate for the purely transverse Weibel instability is determined from relativistic kinetic theory using a waterbag distribution function in the momenta perpendicular to the main propagation direction of the beam. A parametric study is presented for conditions relevant to the fast ignitor. It is shown that for expected parameters the purely transverse Weibel instability will be significantly suppressed or even eliminated due to the transverse energy spread or emittance.

Edge turbulence imaging in the Alcator C-Mod tokamak

Abstract: The two-dimensional (2D) radial vs poloidal structure of edge turbulence in the Alcator C-Mod tokamak [I. H. Hutchinson, R. Boivin, P. T. Bonoli et al., Nucl. Fusion 41, 1391 (2001)] was measured using fast cameras and compared with three-dimensional numerical simulations of edge plasma turbulence. The main diagnostic is gas puff imaging, in which the visible Dα emission from a localized D2 gas puff is viewed along a local magnetic field line. The observed Dα fluctuations have a typical radial and poloidal scale of ≈1 cm, and often have strong local maxima (“blobs”) in the scrape-off layer. The motion of this 2D structure motion has also been measured using an ultrafast framing camera with 12 frames taken at 250 000 frames/s. Numerical simulations produce turbulent structures with roughly similar spatial and temporal scales and transport levels as that observed in the experiment; however, some differences are also noted, perhaps requiring diagnostic improvement and/or additional physics in the numerical m...

Generalized plasma dispersion function for a plasma with a kappa-Maxwellian velocity distribution

Abstract: A generalized plasma dispersion function has previously been obtained for waves in plasmas with isotropic kappa distributions for arbitrary real kappa [Mace and Hellberg, Phys Plasmas 2, 2098 (1995)] In many instances plasmas are found to have anisotropic power-law distributions, and hence a similar dispersion function for electrostatic waves in plasmas having a one-dimensional kappa distribution along a preferred direction in space, and a Maxwellian distribution perpendicular to it has now been developed It is used to study the effect of superthermal electrons and ions on ion-acoustic waves propagating at an angle to a magnetic field This dispersion function should find application to wave studies both in space plasmas, where the magnetic field defines a preferred direction, and in dusty plasma crystal studies, where the ion flow direction is unique

Control of neoclassical tearing modes in DIII–D

Abstract: The development of techniques for neoclassical tearing mode (NTM) suppression or avoidance is crucial for successful high beta/high confinement tokamaks. Neoclassical tearing modes are islands destabilized and maintained by a helically perturbed bootstrap current and represent a significant limit to performance at higher poloidal beta. The confinement-degrading islands can be reduced or completely suppressed by precisely replacing the “missing” bootstrap current in the island O-point or by interfering with the fundamental helical harmonic of the pressure. Implementation of such techniques is being studied in the DIII-D tokamak [J. L. Luxon et al., Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159] in the presence of periodic q=1 sawtooth instabilities, a reactor relevant regime. Radially localized off-axis electron cyclotron current drive (ECCD) must be precisely located on the island. In DIII-D the plasma control system is put into a “search ...

Cross-field blob transport in tokamak scrape-off-layer plasmas

Abstract: Recent measurements show that nondiffusive, intermittent transport of particles can play a major role in the scrape-off-layer (SOL) of fusion experiments. A possible mechanism for fast convective plasma transport is related to the plasma filaments or “blobs” observed in the SOL with fast cameras and probes. In this paper, physical arguments suggesting the importance of blob transport [S. I. Krasheninnikov, Phys. Lett. A 283, 368 (2001)] have been extended by calculations using a three-field fluid model, treating the blobs as coherent propagating structures. The properties of density, temperature and vorticity blobs, and methods of averaging over ensembles of blobs to get the average SOL profiles, are illustrated. The role of ionization of background neutrals in sustaining the density blob transport is also discussed. Many qualitative features of the experiments, such as relatively flat density profiles and transport coefficients increasing toward the wall, are shown to emerge naturally from the blob trans...

Erratum: “Neoclassical conductivity and bootstrap current formulas for general axisymmetric equilibria and arbitrary collisionality regime” [Phys. Plasmas 6, 2834 (1999)]

Abstract: Reference CRPP-ARTICLE-2002-025doi:10.1063/1.1517052View record in Web of Science Record created on 2008-04-16, modified on 2017-05-12

Collision processes of CHy and CHy+ hydrocarbons with plasma electrons and protons

Abstract: The critical fusion reactor design issue of tritium codeposition in tokamaks with carbon as wall material is closely linked with the plasma chemistry involving hydrocarbons. A complete set of cross sections for all important electron- and proton-impact processes with CHy (y=1–4) hydrocarbon impurities and their ions CHy+ is presented. The cross sections are derived on the basis of most recent experimental information and well established cross section scaling relationships. The cross sections are presented in closed analytic forms convenient for implementation in plasma simulation codes.

Numerical study of fast ignition of ablatively imploded deuterium–tritium fusion capsules by ultra-intense proton beams

Abstract: Compression and ignition of deuterium–tritium fuel under conditions relevant to the scheme of fast ignition by laser generated proton beams [Roth et al., Phys. Rev. Lett. 86, 436 (2001)] are studied by numerical simulation. Compression of a fuel containing spherical capsule driven by a pulse of thermal radiation is studied by a one-dimensional radiation hydrodynamics code. Irradiation of the compressed fuel by an intense proton beam, generated by a target at distance d from the capsule center, and subsequent ignition and burn are simulated by a two-dimensional code. A robust capsule, absorbing 635 kJ of 210 eV (peak) thermal x rays, with fusion yield of almost 500 MJ, has been designed, which could allow for target gain of 200. On the other hand, for a reasonable proton spectrum the required proton beam energy Eig, exceeds 25 kJ (for d=4 mm), even neglecting beam losses in the hohlraum and assuming that the beam can be focused on a spot with radius of 10 μm. The effects of proton range lengthening due to ...

Effective screened potentials of strongly coupled semiclassical plasma

Abstract: The pseudopotentials of particle interaction, taking into account both quantum-mechanical effects of diffraction at short distances, and also screening field effects at large distances are obtained for a strongly coupled semiclassical plasma. The limiting cases of potentials are considered.

Filamented transport of laser-generated relativistic electrons penetrating a solid target

Abstract: The paraxial propagation of a relativistic electron beam in a solid target is examined, within a three-dimensional model of particles interacting with the target electron return current via a diffusive electromagnetic field. Simulations of a modulated beam show amplification of the modulation seed, with growth rates comparing reasonably well with the linear analysis of the model. Scenarios of beam fragmentation are observed and discussed in more realistic conditions, when beam collisions on both target ions and electrons and the resulting solid heating and ionization are taken into account.

Nonstationarity of strong collisionless quasiperpendicular shocks: Theory and full particle numerical simulations

Abstract: Whistler waves are an intrinsic feature of the oblique quasiperpendicular collisionless shock waves. For supercritical shock waves, the ramp region, where an abrupt increase of the magnetic field occurs, can be treated as a nonlinear whistler wave of large amplitude. In addition, oblique shock waves can possess a linear whistler precursor. There exist two critical Mach numbers related to the whistler components of the shock wave, the first is known as a whistler critical Mach number and the second can be referred to as a nonlinear whistler critical Mach number. When the whistler critical Much number is exceeded, a stationary linear wave train cannot stand ahead of the ramp. Above the nonlinear whistler critical Mach number, the stationary nonlinear wave train cannot exist anymore within the shock front. This happens when the nonlinear wave steepening cannot be balanced by the effects of the dispersion and dissipation. In this case nonlinear wave train becomes unstable with respect to overturning. In the present paper it is shown that the nonlinear whistler critical Mach number corresponds to the transition between stationary and nonstationary dynamical behavior of the shock wave. The results of the computer simulations making use of the 1D full particle electromagnetic code demonstrate that the transition to the nonstationarity of the shock front structure is always accompanied by the disappearance of the whistler wave train within the shock front. Using the two-fluid MHD equations, the structure of nonlinear whistler waves in plasmas with finite beta is investigated and the nonlinear whistler critical Mach number is determined. It is suggested a new more general proof of the criteria for small amplitude linear precursor or wake wave trains to exist.

Obliquely propagating electron-acoustic solitary waves

Abstract: A theoretical investigation is carried out for understanding the properties of obliquely propagating electron-acoustic solitary waves (EASWs) in a magnetized plasma whose constituents are a cold magnetized electron fluid, hot electrons obeying a vortex-like distribution, and stationary ions. It is found that the present plasma model supports EASWs having a positive potential, which corresponds to a dip (hump) in the cold (hot) electron number density. The effects of the external magnetic field and the obliqueness are found to significantly change the basic properties (viz. the amplitude and the width) of the EASWs. The present investigation can be of relevance to the electrostatic solitary structures observed in various space plasma environments (viz. the cusp of the terrestrial magnetosphere, the geomagnetic tail, the auroral regions, etc.).

Alfvén wave cascades in a tokamak

Abstract: Experiments designed for generating internal transport barriers in the plasmas of the Joint European Torus [JET, P. H. Rebut et al., Proceedings of the 10th International Conference, Plasma Physics and Controlled Nuclear Fusion, London (International Atomic Energy Agency, Vienna, 1985), Vol. I, p. 11] reveal cascades of Alfven perturbations with predominantly upward frequency sweeping. These experiments are characterized by a hollow plasma current profile, created by lower hybrid heating and current drive before the main heating power phase. The cascades are driven by ions accelerated with ion cyclotron resonance heating (ICRH). Each cascade consists of many modes with different toroidal mode numbers and different frequencies. The toroidal mode numbers vary from n=1 to n=6. The frequency starts from 20 to 90 kHz and increases up to the frequency range of toroidal Alfven eigenmodes. In the framework of ideal magnetohydrodynamics (MHD) model, a close correlation is found between the time evolution of the Alfven cascades and the evolution of the Alfven continuum frequency at the point of zero magnetic shear. This correlation facilitates the study of the time evolution of both the Alfven continuum and the safety factor, q(r), at the point of zero magnetic shear and makes it possible to use Alfven spectroscopy for studying q(r). Modeling shows that the Alfven cascade occurs when the Alfven continuum frequency has a maximum at the zero shear point. Interpretation of the Alfven cascades is given in terms of a novel-type of energetic particle mode localized at the point where q(r) has a minimum. This interpretation explains the key experimental observations: simultaneous generation of many modes, preferred direction of frequency sweeping, and the absence of strong continuum damping.

Sustained rotational stabilization of DIII-D plasmas above the no-wall beta limit

Abstract: Sustained stabilization of the n=1 kink mode by plasma rotation at beta approaching twice the stability limit calculated without a wall has been achieved in DIII-D by a combination of error field reduction and sufficient rotation drive. Previous experiments have transiently exceeded the no-wall beta limit. However, demonstration of sustained rotational stabilization has remained elusive because the rotation has been found to decay whenever the plasma is wall stabilized. Recent theory [Boozer, Phys. Rev. Lett. 86, 5059 (2001)] predicts a resonant response to error fields in a plasma approaching marginal stability to a low-n kink mode. Enhancement of magnetic nonaxisymmetry in the plasma leads to strong damping of the toroidal rotation, precisely in the high-beta regime where it is needed for stabilization. This resonant response, or “error field amplification” is demonstrated in DIII-D experiments: applied n=1 radial fields cause enhanced plasma response and strong rotation damping at beta above the no wal...

Recent Trident single hot spot experiments: Evidence for kinetic effects, and observation of Langmuir decay instability cascade

Abstract: Single hot spot experiments offer several unique opportunities for developing a quantitative understanding of laser-plasma instabilities. These include the ability to perform direct numerical simulations of the experiment due to the finite interaction volume, isolation of instabilities due to the nearly ideal laser intensity distribution, and observation of fine structure due to the homogeneous plasma initial conditions. Experiments performed at Trident in the single hot spot regime have focused on the following issues. First, the intensity scaling of stimulated Raman scattering (SRS) for classically large damping regimes (kλD=0.35) was examined, and compared to classical SRS theory. SRS onset was observed at intensities much lower than expected (2×1015 W/cm2), from which nonclassical damping is inferred. Second, Thomson scattering was used to probe plasma waves driven by SRS, and structure was observed in the scattered spectra consistent with multiple steps of the Langmuir decay instability. Finally, sca...

Parallel electric fields in the upward current region of the aurora: Indirect and direct observations

Abstract: In this article we present electric field, magnetic field, and charged particle observations from the upward current region of the aurora focusing on the structure of electric fields at the boundary between the auroral cavity and the ionosphere. Over 100 high-resolution measurements of the auroral cavity that were taken by the Fast Auroral Snapshot (FAST) satellite are included in this study. The observations support earlier models of the auroral zone that held that quasi-static parallel electric fields are the primary acceleration mechanism. In addition to the statistical study, several examples of direct observations of the parallel electric fields at the low-altitude boundary of the auroral cavity are put forth. These observations suggest that the parallel electric fields at the boundary between the auroral cavity and the ionosphere are self-consistently supported as oblique double layers.

Fractional kinetics for relaxation and superdiffusion in a magnetic field

Abstract: Fractional Fokker–Planck equation is proposed for the kinetic description of relaxation and superdiffusion processes in constant magnetic and random electric fields. It is assumed that the random electric field acting on a test charged particle is isotropic and possesses non-Gaussian Levy stable statistics. These assumptions provide one with a straightforward possibility to consider formation of anomalous stationary states and superdiffusion processes, both properties are inherent to strongly nonequilibrium plasmas of solar systems and thermonuclear devices. The fractional kinetic equation is solved, the properties of the solution are studied, and analytical results are compared with those of numerical simulation based on the solution of the Langevin equations with a noise source having Levy stable probability density. It is found, in particular, that the stationary states are essentially non-Maxwellian ones and, at the diffusion stage of relaxation, the characteristic displacement of a particle grows superdiffusively with time and is inversely proportional to the magnetic field.

Modeling of stochastic magnetic flux loss from the edge of a poloidally diverted tokamak

Abstract: A field line integration code is used to study the loss of edge poloidal magnetic flux due to stochastic magnetic fields produced by an error field correction coil (C–coil) in DIII–D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] for various plasma shapes, coil currents and edge magnetic shear profiles. We find that the boundary of a diverted tokamak is more sensitive to stochastic flux loss than a nondiverted tokamak. The C–coil has been used to produce a stochastic layer in an ohmic diverted discharge with characteristics similar to those seen in stochastic boundary experiments in circular limiter ohmic plasmas, including (1) an overall increase in recycling, (2) a broadening of the recycling profile at the divertor, and (3) a flattening of the boundary profiles over the extent of the stochastic layer predicted by the field line integration code. Profile flattening consistent with field line integration results is also seen in some high performance discharges with edge transport barriers. The prediction of ...

Characteristics of parallel electric fields in the downward current region of the aurora

Abstract: Direct measurements of parallel electric fields suggest that they are, in part, self-consistently supported as strong double layers in the auroral downward current region. The observed parallel electric fields have amplitudes reaching nearly 1 V/m and are confined to a thin layer of approximately 10 Debye lengths. The structures are moving at roughly the ion acoustic speed in the direction of the accelerated electrons, i.e., anti-earthward. On the high-potential side of the parallel electric field there is a clear signature of an accelerated electron beam which rapidly plateaus within a few hundred Debye lengths from the parallel electric field. Strong wave turbulence is observed in the vicinity of the plateaued electron distribution. Fast solitary waves, identified as a signature of electron phase-space holes, are seen farther away from the parallel electric field on the high-potential side. The observed ion distributions also indicate the presence of the parallel electric field. On the low-potential sid...

Indirect-drive noncryogenic double-shell ignition targets for the National Ignition Facility: Design and analysis

Abstract: Analysis and design of indirect-drive National Ignition Facility double-shell targets with hohlraum temperatures of 200 eV and 250 eV are presented. The analysis of these targets includes the assessment of two-dimensional radiation asymmetry and nonlinear mix. Two-dimensional integrated hohlraum simulations indicate that the x-ray illumination can be adjusted to provide adequate symmetry control in hohlraums specially designed to have high laser-coupling efficiency [Suter et al., Phys. Plasmas 7, 2092 (2000)]. These simulations also reveal the need to diagnose and control localized 10–15 keV x-ray emission from the high-Z hohlraum wall because of strong absorption by the high-Z inner shell. Preliminary estimates of the degree of laser backscatter from an assortment of laser–plasma interactions suggest comparatively benign hohlraum conditions. The application of a variety of nonlinear mix models and phenomenological tools, including buoyancy-drag models, multimode simulations and fall-line optimization, in...

Beyond the Child–Langmuir law: A review of recent results on multidimensional space-charge-limited flow

Abstract: Space-charge-limited (SCL) flows in diodes have been an area of active research since the pioneering work of Child and Langmuir in the early part of the last century. Indeed, the scaling of current density with the voltage to the 3/2’s power is one of the best-known limits in the fields of non-neutral plasma physics, accelerator physics, sheath physics, vacuum electronics, and high power microwaves. In the past five years, there has been renewed interest in the physics and characteristics of SCL emission in physically realizable configurations. This research has focused on characterizing the current and current density enhancement possible from two- and three-dimensional geometries, such as field-emitting arrays. In 1996, computational efforts led to the development of a scaling law that described the increased current drawn due to two-dimensional effects. Recently, this scaling has been analytically derived from first principles. In parallel efforts, computational work has characterized the edge enhancement of the current density, leading to a better understanding of the physics of explosive emission cathodes. In this paper, the analytic and computational extensions to the one-dimensional Child–Langmuir law will be reviewed, the accuracy of SCL emission algorithms will be assessed, and the experimental implications of multidimensional SCL flows will be discussed.

Deceleration phase of inertial confinement fusion implosions

Abstract: A model for the deceleration phase and marginal ignition of imploding capsules is derived by solving a set of ordinary differential equations describing the hot-spot energy balance and the shell dynamics including the return shock propagation. It is found that heat flux leaving the hot spot goes back in the form of internal energy and PdV work of the material ablated off the inner-shell surface. Though the hot-spot temperature is reduced by the heat conduction losses, the hot-spot density increases due to the ablated material in such a way that the hot-spot pressure is approximately independent of heat conduction. For hot-spot temperatures exceeding approximately 7 keV, the ignition conditions are not affected by heat conduction losses that are recycled into the hot spot by ablation. Instead, the only significant internal energy loss is due to the hot-spot expansion tamped by the surrounding shell. The change of adiabat induced by the shock is also calculated for marginally igniting shells, and the relati...

Characteristics of an atmospheric microwave-induced plasma generated in ambient air by an argon discharge excited in an open-ended dielectric discharge tube

Abstract: Parametric observations on an atmospheric-pressure plasma sustained in ambient air by an argon discharge excited by 2.45 GHz microwaves in an open-ended dielectric discharge tube are reported. Microwave power, discharge tube dimensions, and argon flow rate were the major operating parameters. Three distinctive plasma regions were observed: plasma filaments exiting from the discharge tube, converging point of these filaments, and a plasma flame. At the filament-converging point, argon atom excitation temperature, rotational temperature, and electron density were measured by optical emission spectroscopy (OES) in the operating range of (3.0–5.0) liters per minute of gas flow rate and (650–950) W of microwave power. The measured excitation temperature and rotational temperature were (5000–5800) K and (2800–3400) K, respectively. The electron density obtained by Stark broadening width of the Hβ line showed (5.0–8.0)×1014 cm−3. It was observed that the volume of the plasma flame and the gas temperature were increased with increasing the microwave power. On the other hand, higher gas flow rates increased the electron density. In the plasma flame, the gas temperature measured by a thermocouple and OES was in the range of (1030–2200) K, which showed an exponential decrease in the axial direction away from the converging point.

Effects of pulse-length and emitter area on virtual cathode formation in electron guns

Abstract: Recent experiments at the University of Maryland using photoemission from a dispenser cathode have yielded some interesting results regarding the effects of the area of emission and of the ratio between the pulse length and the gap transit time on the amount of current that may be drawn from an electron gun before a virtual cathode forms. The experiments show that a much higher current density may be drawn from a short pulse or limited emitter area than is anticipated by the Child–Langmuir limiting current. There is also evidence that the current may be increased even after virtual cathode formation, which leads a distinction between a limiting current density and a current density critical for virtual cathode formation. The experiments have also yielded some interesting results on the longitudinal structure of the current pulse passed through the anode. Some empirical and theoretical scaling laws regarding the formation of virtual cathodes in an electron gun will be presented. This work was motivated by the needs of the University of Maryland Electron Ring (UMER) [P. G. O’Shea, M. Reiser, R. A. Kishek et al., Nucl. Instrum. Methods Phys. Res. A 464, 646 (2001)] where the goal is to generate pulses that are well-localized in time and space.

How to calculate the neoclassical viscosity, diffusion, and current coefficients in general toroidal plasmas

Abstract: A novel method to obtain the full neoclassical transport matrix for general toroidal plasmas by using the solution of the linearized drift kinetic equation with the pitch-angle-scattering collision operator is shown. In this method, the neoclassical coefficients for both poloidal and toroidal viscosities in toroidal helical systems can be obtained, and the neoclassical transport coefficients for the radial particle and heat fluxes and the bootstrap current with the nondiagonal coupling between unlike-species particles are derived from combining the viscosity-flow relations, the friction-flow relations, and the parallel momentum balance equations. Since the collisional momentum conservation is properly retained, the well-known intrinsic ambipolar condition of the neoclassical particle fluxes in symmetric systems is recovered. Thus, these resultant neoclassical diffusion and viscosity coefficients are applicable to evaluating accurately how the neoclassical transport in quasi-symmetric toroidal systems deviates from that in exactly symmetric systems.