Search

The Advanced Toroidal Facility (ATF) torsatron [Fusion Technol. 10, 179 (1986)] has completed experiments focusing on microwave scattering measurements of density fluctuations and transport studies utilizing the modulation of dimensionless parameters. Microwave scattering measurements of electron density fluctuations in the core of low‐collisionality electron cyclotron heated (ECH) plasmas show features that might be evidence of trapped electron instabilities. Starting from gyro‐Bohm scaling, the additional dependence of confinement on the dimensionless parameters ν* and β (collisionality and beta) has been investigated by modulating each of these parameters separately, revealing the additional favorable dependence, τE∝τgBν*−0.18β+0.3.

Fast wave heating experiments in the ion cyclotron range of frequencies (ICRF) were performed on target plasmas produced by 350 kW of electron cyclotron heating at 53 GHz and also by neutral beam injection in the Advanced Toroidal Facility (ATF). Various heating regimes were investigated in the frequency range between 9.2 MHz and 28.8 MHz with magnetic fields of 0.95 T and 1.9 T on axis. The nominal pulse lengths of up to 200 kW RF power were in the range between 100 and 400 ms. Data from spectroscopy, loading measurements, and edge RF and Langmuir probes were used to characterize the RF induced effects on the ATF plasma. In the hydrogen minority regime at low plasma density, large suprathermal ion tails were observed with a neutral particle analyser. At high density (ne ≥ 5.0 × 1013 cm-3) substantial increases in antenna loading were observed, but ICRF power was insufficient to produce definitive heating results. A two-dimensional RF heating code, ORION, and a Fokker-Planck code, RFTRANS, were used to simulate these experiments. A simulation of future high power, higher density experiments in ATF indicates improved bulk heating results due to the improved loading and more efficient thermalization of the minority tail

Recent experiments in the Advanced Toroidal Facility (ATF) [Fusion Technol. 10, 179 (1986)] have been directed toward investigations of the basic physics mechanisms that control confinement in this device. Measurements of the density fluctuations throughout the plasma volume have provided indications for the existence of theoretically predicted dissipative trapped electron and resistive interchange instabilities. These identifications are supported by results of dynamic configuration scans of the magnetic fields during which the magnetic well volume, shear, and fraction of confined trapped particles are changed continuously. The influence of magnetic islands on the global confinement has been studied by deliberately applying error fields which strongly perturb the nested flux‐surface geometry, and the effects of electric fields have been investigated by means of biased limiter experiments.

The spectral line emissions from impurities injected using the laser ablation technique have been modelled in order to deduce impurity transport coefficients in the Advanced Toroidal Facility (ATF). The transport is found to be mainly diffusive, with little or no convective component. To reproduce the observed line emission it is necessary to postulate a radially dependent diffusion coefficient. For plasmas heated by electron cyclotron frequency waves the impurity transport is best fitted with a diffusion coefficient of 1000 cm2/s in the centre, increasing to 5000 cm2/s at the plasma edge. The global impurity particle confinement time for these plasmas is 65 ms and is considerably larger than the corresponding energy confinement time. Plasmas heated by high energy neutral particle beams display different impurity transport, with the best fit being a diffusion coefficient that is peaked on axis (5000 cm2/s) and that decreases towards larger minor radii (500 cm2/s at the plasma boundary). These transport coefficients have been successfully used to simulate the evolution of intrinsic impurities as well as laser ablated impurities in ATF

Various wall conditioning techniques have been used on the Advanced Toroidal Facility (ATF). Continued improvement in plasma parameters has been obtained. In ATF, a stellarator, wall conditioning is more important for obtaining favorable plasma parameters than it is in plasma devices with current. Discharge cleaning, baking, and gettering with both chromium and titanium have been used as conditioning techniques. Gettering with titanium has increased the pumping speed of nitrogen and oxygen by more than a factor of 10, significantly reducing impurity effects, and has allowed better control over wall recycling and thereby plasma density. This has increased the operating space for many of the plasma parameters. The effects of these conditioning techniques on plasma parameters are discussed.

The characteristics of plasmas in the Advanced Toroidal Facility (ATF) have proven to be strongly dependent on the type of wall conditioning employed. A succession of techniques, beginning with glow discharge cleaning and baking, and evolving to gettering with chromium and titanium, have led to progressive improvement of the plasma parameters. Gettering with titanium has reduced the low-Z impurity content by a factor of 3, lowered the radiated power by a factor of 2.5–3.5, and improved the control over the electron density. The maximum values achieved for stored energy, line averaged density and confinement times are 28 kJ, 1.2 × 1014cm−3 and 25 ms, respectively. These parameters are comparable to the best results achieved in the ISX-B tokamak which had the same average minor radius and one half the major radius of ATF. Quasi-steady operation for 200 ms of neutral beam injection (NBI) has been obtained in high density, titanium gettered plasmas without the collapses that were typical earlier periods of operation. Neon injection experiments have helped to delineate the limits on the global levels of radiation that can be maintained and have supported the conclusion that mechanisms other than radiative losses are important for initiating the collapses still observed in low density NBI plasmas.

An overview of recent AFT (Advanced Toroidal Facility) experimental results and program plans is presented, with emphasis on the role of magnetic configuration controls in transport studies. The ATF operating space is bounded by a density limit that effectively sets a limit on the energy confinement time tau /sub E/. Although this limit is not solely due to impurities, it has recently been raised by improved cleanliness following titanium gettering. This has led to collapse-free neutral beam injection discharges with global tau /sub E/ approximately=16 ms. Preliminary experiments show that stored energy and bootstrap current are sensitive to details of the magnetic configuration. >

Plasmas in the Advanced Toroidal Facility (ATF), an l = 2 torsatron with 12 field periods, are produced by 200–400 kW of electron cyclotron heating (ECH) and up to 1.5 MW of neutral-beam injection (NBI). The characteristics of the plasmas are sensitive to the type of wall conditioning employed. A progression of techniques, beginning with glow discharge cleaning and baking and evolving to gettering with chromium and titanium, has significantly reduced the low-Z impurity content, lowered the fraction of radiated power, and permitted improved control over the electron density. As a result, plasma-parameters and machine performance have been enhanced significantly. The maximum values achieved for stored energy, line-averaged density, and confinement times are 28 kJ, 1.2 × 1020m−3, and 25 ms. These parameters are comparable to those obtained in the ISX-B tokamak. In addition, with titanium gettering, quasisteady operation for 200 ms of neutral beam injection has been obtained without the collapses that characterized earlier periods of operation.

Experiments involving plasma improvement, confinement scaling, bootstrap currents, and edge fluctuations have been carried out in the Advanced Toroidal Facility (ATF) torsatron [Fusion Technol. 10, 179 (1986)]. Average densities ne≤9×1019 m−3 have been obtained, with global energy confinement times τ*E≤20 msec. Confinement times generally follow the stellarator/torsatron empirical scaling law, τSL =0.17×P−0.58n0.69eB0.84a2R0.75 (with τSL in seconds, power P in megawatts, density ne in 1020 m−3, and plasma radius a and major radius R in meters). Gas injection during neutral beam injection (NBI) causes increases in ne, so that τ*E does not decrease during NBI. Edge plasma fluctuations are found to exhibit a mode change near the peak of the energy confinement time. Plasma currents observed during electron cyclotron heating have been identified as bootstrap currents.

The poloidal momentum balance equation in tokamaks is shown to have bifurcated solutions; the poloidal flow velocity Up can suddenly become more positive when the ion collisionality decreases. The corresponding radial electric field Er becomes more negative, suppresses turbulent fluctuations, and improves plasma confinement. A heuristic argument is employed to illustrate the effects of Er on turbulent fluctuations. A more negative value of Er and/or a more positive value of dEr /dr can suppress the fluctuation amplitudes, if dP/dr

Access to the magnetohydrodynamic (MHD) second stability regime has been achieved in the Advanced Toroidal Facility (ATF) torsatron [Fusion Technol. 10, 179 (1986)]. Operation with a field error that reduced the plasma radius and edge rotational transform resulted in peaked pressure profiles and increased Shafranov shift that lowered the theoretical transition to ideal MHD second stability to β0≊1.3%; the experimental β values (β0≤3%) are well above this transition. The measured magnetic fluctuations decrease with increasing β, and the pressure profile broadens, consistent with the theoretical expectations for self‐stabilization of resistive interchange modes. Initial results from experiments with the field error removed show that the pressure profile is now broader. These later discharges are characterized by a transition to improved (×2–3) confinement and a marked change in the edge density fluctuation spectrum, but the causal relationship of these changes is not yet clear.

In stellarators, external coil currents rather than internal currents are used to produce the confinement fields. This allows for greater flexibility in the design and operation of a stellarator. This flexibility can be exploited in a series of experiments on one device, such as the ATF. MHD stability boundaries will be tested by varying the vertical field. Access to the second stability regime has been observed in initial experiments on ATF. In this regime, the relationship between stabilization of pressure-driven modes and transport improvement can be studied. The density profile peaking factor can be varied using pellet injection in order to understand the role of eta /sub j/ modes. As an example, the ATF-TEXT collaboration on edge fluctuations will compare the levels of resistive-gradient-driven fluctuations observed in the two devices. In addition, global confinement and local transport comparisons have been made to tokamaks and to other stellarators of roughly similar size and capabilities but with widely varying configuration properties. >

Measurements of the effective charge Z{sub eff} in plasmas with electron cyclotron heating (ECH) and neutral beam injection (NBI) in the Advanced Toroidal Facility (ATF) have been carried out using visible bremsstrahlung. The electron temperature needed for the analysis is calculated from the measured stored energy and electron density. The value of Z{sub eff} varies widely depending on experimental conditions. In ECH plasmas it is between 2 and 8. In NBI plasmas, which are subject to radiation collapse, Z{sub eff} is between 3 and 5 at the time the stored energy reaches a maximum. However, Z{sub eff} is less than 2.5 in quasi-steady medium-density plasmas and is close to 1.2 in the highest-density plasmas, where the average electron density {bar n}{sub e} is of the order of 10{sup 14} cm{sup {minus}3}. 12 refs., 29 figs., 1 tab.

An overview of recent experimental results from the Advanced Toroidal Facility (ATF) is presented. Beam-heated plasmas with {bar n}{sub e} of 10{sup 20} m{sup {minus}3} and {tau}{sub E}{asterisk} of {approx}20 ms have been achieved. Thermal collapse of the plasmas is mitigated by wall conditioning and particle fueling. Confinement time scales positively with density and magnetic field, offsetting deterioration with power. Results fit the LHD scaling and the drift wave turbulence scaling. Bootstrap currents observed during ECH agree with neoclassical theory in magnitude and parameter dependences. Fast reciprocating Langmuir probe measurements show that edge fluctuations in ATF have many similarities to those in the TEXT tokamak. The location of {tilde B} instabilities has shifted outward in radius, consistent with the broader pressure profiles. 14 refs., 6 figs.

Several forbidden lines of titanium have recently become strong enough to be identified in ATF plasmas in the ultraviolet and in the visible. The increase in intensity has resulted from gettering of the vacuum vessel with titanium both to suppress light impurities and to control hydrogen recycling. Three orders of the forbidden Ti xiv line at 2117.1 A have been observed in vacuum, and the second and third orders have been observed in air using two different Czerny–Turner spectrometers. Doppler broadening of this line has been used to infer ion temperatures in the interior of ATF plasmas. These data supplement ion temperature measurements employing lines from carbon, nitrogen, and oxygen reported earlier [R. C. Isler et al., Nucl. Fusion 29, 1391 (1989)]. Tentative identifications of other forbidden lines such as Ti vii at 1938.4 A, Ti xv at 2544.8 A, Ti xvii at 3370.8 A and 3834.4 A, and Ti xviii at 1778.1 A have also been made. Research was sponsored by the Office of Fusion Energy, U.S. Department of Ene...

A variational principle is developed for computing accurate values of local plasma transport coefficients in nonsymmetric toroidal confinement configurations. Numerical solutions of the linearized drift Fokker–Planck equation are used to obtain the thermodynamic fluxes as functions of collision frequency and the radial electric field. Effects resulting from the variation of the longitudinal adiabatic invariant J along an orbit (resulting from particle transitions from helically trapped to toroidally trapped orbits) are treated. The velocity‐space distribution resulting from trapped, circulating, and transition particle orbits is well represented by a Legendre polynomial expansion in the pitch angle coordinate. The computational effort is significantly reduced from that required with Monte Carlo methods through use of an efficient treatment of the disparity between the time scales of collisionless and collisional particle dynamics. Numerical computations for a stellarator configuration are presented.

Stellarator transport scalings with electric field, geometry, and collision frequency in the reactor‐relevant collisionless‐detrapping regime are determined from numerical solutions of the drift kinetic equation. A new geometrical scaling, proportional to e3/2t rather than ete1/2h, is found, where et is the inverse aspect ratio and eh is the helical ripple. With the new scaling, no reduction in energy confinement time is associated with large helical ripple, which provides design flexibility. Integral expressions for the particle and heat fluxes that are useful for transport simulations are given.

Detailed studies of spectra from the ISX-$A$ (Impurity Study Experiment) tokamak at the Oak Ridge National Laboratory have shown that certain oxygen-ion lines appear too anomalously intense to have been excited solely by electron collisions. These results are interpreted as being due to charge transfer and suggest the necessity of incorporating this mechanism into analyses of tokamak plasmas.

Wall conditioning and chromium gettering have reduced Zeff in the Advanced Toroidal Facility (ATF) to the range of 1.5−2.2. As a result, it is possible to achieve essentially steady state conditions using electron cyclotron heating alone, without the uncontrolled growth of the electron and impurity densities observed in the very earliest discharges, which always collapsed to low temperature afterglows. Plasma collapses are, however, still observed during neutral beam injection. It is known that large islands have been present in ATF during its initial periods of operation, but it cannot be determined whether they influence any aspect of the collapse. The impurity behaviour and the radiation losses in this perturbed magnetic configuration are discussed.

Observations of radiation from iron and from argon used as a test gas indicate that co-injection inhibits impurity accumulation in the interior of ISX-B discharges, but counter-injection enhances accumulation. These results agree qualitatively with recent theoretical calculations.

Recent calculations have shown that when external momentum sources and plasma rotation are included in the neoclassical theory, the standard results for impurity transport can be strongly altered. Under appropriate conditions, inward convection is reduced by co-injection and enhanced by counter-injection. In order to examine the theoretical predictions, several observations of impurity transport have been made in the ISX-B tokamak during neutral-beam injection for comparison with the transport seen with Ohmic heating alone. Both intrinsic contaminants and deliberately introduced test impurities display a behaviour that is in qualitative agreement with the predicted beam-driven effects. These correlations are particularly noticeable when the comparisons are made for deuterium where the impurity transport in the Ohmically heated discharges exhibits neoclassical-like characteristics, i.e. accumulation and long confinement times. Similar but smaller effects are observed in beam-heated hydrogen discharges; neoclassical-like behaviour is not seen in Ohmically heated hydrogen sequences. Emphasis has been placed on measuring toroidal plasma rotation, and semi-quantitative comparisons with the theories of beam-induced impurity transport have been made. It is possible that radial electric fields other than those associated with momentum transfer and increased anomalous processes during injection could also play a role.

Nitrogen has been puffed into the Impurity Study Experiment (ISX-B) tokamak as a test gas for evaluating the effect of pump limiters on impurity control. The gas is introduced either through a nozzle at the limiter tip or from a location at the wall of the vacuum chamber. The interior nitrogen content is monitored by charge-exchange excitation of N VII lines and depends only slightly on the location of the N2 source or on whether the pumps are activated or not. The edge radiation from NIV is also affected little by activating the pumps when the source is at the limiter tip, but is strongly influenced when the source is at the wall location. The spectral data suggest that the reservoir of nitrogen in the scrape-off layer is efficiently pumped while the nitrogen content of the main plasma is not affected. The implication is that, in the quasi-steady interval of a discharge, radial diffusion is very slow compared to parallel transport in the vicinity of the limiter tip.

During neutral-beam-heated, counter-injection discharges in the ISX-$B$ tokamak, impurities tend to collect in the interior of the plasmas. In these circumstances iron ions preferentially accumulate with long confinement times in regions of almost constant electron temperature. The concentrations of intermediate stages of iron (Fe XV, XVI, XVIII, and XIX) have been studied under these conditions to investigate the ratios of recombination and ionization coefficients. The dielectronic recombination coefficients are then deduced by assuming that the ionization and the radiative and charge-exchange recombination rates can be calculated closely from theory.

The particle and heat flux problems in the collisional or Pfirsch-Schluter regime for a two-ion-species tokamak plasma are solved by using a kinetic approach with exact Fokker-Planck collision operators. These solutions are appropriate for analysing the behaviour of impurities in the low-temperature plasma edge region where impurities first enter the plasma from the outside. We find that low-charge states of low-mass impurities can be screened effectively from further penetration of the plasma.

Target plasmas for neutral beam injection (NBI) in the Advanced Toroidal Facility (ATF) are formed using approximately 200 kW of 53 GHz electron cyclotron heating (ECH). During the early operational period of this device, field errors existed which produced large islands at the ι = 1/2 surface and several smaller, but non-negligible closely spaced islands at larger radii. The evolution of typical plasma parameters during NBI into plasmas produced in this perturbed magnetic configuration is discussed. The ion temperatures near the centre of the ECH target plasmas, as measured from Doppler broadening of impurity lines, are approximately 100 eV, and the central electron temperatures are close to 800 eV. NBI at powers up to 1.4 MW characteristically raises Tj(O) by factors of two to three for 50−80 ms, but thereafter the ion temperature decays. The electron temperature is not raised by NBI above its level in the ECH plasmas; it typically drops monotonically from the start of injection. Both the Ti and the Te profiles indicate the existence of a low temperature region from the ι = 1/2 surface (ρ = 0.6) to the plasma edge, apparently because of the island structure, and modelling suggests that the plasma collapse may be caused by the peculiar radiation profile which develops under these conditions. However, whether the characteristics of the temperature profiles and the collapse can truly be ascribed to the existence of the islands can be decided only after repair of the field errors.

Bootstrap currents in the low collisionality regime in nonaxisymmetric toroidal plasmas are calculated analytically using a model drift kinetic equation. The results obtained using the analytic expression are compared with those calculated from the numerical solutions of the drift kinetic equation. Qualitatively and quantitively, the results are in reasonable agreement.

Variations of the intensities of spectral lines are utilized to determine the extent to which the impurity concentrations of ORMAK-produced plasmas are altered by neutral-beam injection and, in some cases, by the simultaneous introduction of a puff of hydrogen. Concurrent variations of oxygen emissions resulting from alterations in the profiles of electron temperatures and concentrations are taken into account through solving the coupled continuity equations of the several ionic species of this element. Ad-hoc transport velocities are utilized and a complete re-cycling model is assumed.

It is shown that the poloidal momentum balance equation in tokamaks has bifurcated solutions. The poloidal flow velocity ${U}_{p}$ can suddenly become more positive when the ion collisionality decreases. The corresponding radial electric field ${E}_{r}$ becomes more negative and hence suppresses the turbulent fluctuations. Thus, plasma confinement is improved. The theory is employed to explain the L-H transition observed in tokamaks.

Stimulated by the necessity of numerically integrating the one-dimensional, first-order, magnetic-flux-surface-averaged particle continuity equation to study impurity transport in tokamaks, we have investigated how to obtain estimates of functions and their first derivatives correct to second order in the grid spacing for arbitrary grids. Using integral-averaged values with arbitrary weight functions, we readily find two-term linear approximations to the functions that satisfy the accuracy criterion. However, in the case of two-term linear approximations to the first derivative, we find that the grid partition must satisfy a nodal equation to obtain the desired accuracy. When the entire grid cannot be set up to satisfy the nodal equation, transitions involving three-term linear approximations to the derivative are required. We also determine the point between two grid points at which the integral-averaged function value can be identified with the function evaluated at that point. Finally, we give examples of grid selection for two different weight functions: w = 1 and w = r.

We find, using a time-dependent coronal model, that radiation from stationary (i.e., non-diffusing) low Z impurities cannot account for the experimentally observed radiation losses in tokamaks, whereas recycling low Z impurities might. Thus, we infer from this and other circumstantial evidence that impurities recycle from the wall into the plasma and out again, on time scales not much longer than the energy containment time. The (neo)classical influx of impurities provides an inward transport mechanism; the outward transport process is unknown. However, a recent and more exact (no mass ratio expansion) impurity transport calculation1has shown that a “temperature-screening” effect may inhibit or reverse at least the influx of low charge states of low mass impurities. Another quandry occurs in gas puffing experiments where the electron density at the plasma center rises rapidly. We have investigated neutral transport in the plasma edge in a number of different models, including an ANISN-type (NUTRLSN) transport code. The effects considered include geometry, energy-cascading, reflection and a proper accounting of the (small) power lost via charge-exchange. We find that the observed density rise cannot be explained by a combination of neutral influx and particle diffusion. In order to resolve these quandries relating to the plasma edge, we hypothesize a “new” transport model based on the developing, generalized theory of dissipative trapped-electron instabilities. In this model, the anomalous transport adds to neoclassical transport and affects only the “cross-field” processes. In the resultant model the electron temperature is determined by the anomalous electron heat transport, as usual. However, the particle density is determined by balancing the inward Ware pinch with the outward anomalous particle diffusion; the impurity density results from balancing the inward classical diffusion against the outward anomalous diffusion. The inward Ware pinch is found to be sufficiently rapid to explain the density increases observed in ORMAK gas puffing experiments and in ALCATOR up to 3 × 1014 cm−3.

A recent review article by Hirshman and Sigmar includes expressions needed to calculate the parallel friction coefficients, the essential ingredients of the plateau-Pfirsch-Schluter transport coefficients, using the method of reduced charge states. These expressions have been collected and an expanded notation introduced in some cases to facilitate differentiation between reduced charge state and full charge state quantities. A form of the Coulomb logarithm relevant to the method of reduced charge states is introduced. This method of calculating the f/sub ij//sup ab/ has been implemented in the impurity transport simulation code IMPTAR and has resulted in an overall reduction in computation time of approximately 25% for a typical simulation of impurity transport in the Impurity Study Experiment (ISX-B). Results obtained using this treatment are almost identical to those obtained using an earlier approximate theory of Hirshman.

To simulate multispecies impurity transport in tokamaks, a set of coupled continuity equations including source and sink terms from atomic processes (rate terms) were solved numerically. The diffusion and rate terms are integrated separately in time using a fractional step-splitting technique which is accurate to second order in the time step. Calculations were performed treating individually all the ionization stages of oxygen and iron impurities in a hydrogen plasma. Calculated O VI and O VII relative density profiles agree qualitatively with profiles measured in the Adiabatic Toroidal Compressor (ATC) tokamak when purely neoclassical diffusion coefficients are used.

Electron cyclotron heating (ECH) experiments in the Advanced Toroidal Facility (ATF) torsatron exploit unique capabilities for external control of the magnetic configuration and long‐pulse operation. The ECH power deposition profile is determined from the change of the electron temperature profiles during ECH power turn‐off and from power modulation. The measured dependence of absorbed power on the magnetic field agrees well with that obtained from ray tracing calculations for first‐pass and multiple‐bounce absorption. In ATF, parameters of basic physics interest (magnetic shear, magnetic well/hill, and contained trapped particle fraction) have been varied dynamically during a single long‐pulse (up to 20‐s) discharge (dynamic configuration control). Varying a single physics parameter while keeping others fixed elucidates the parameter’s influence on plasma behavior. Modulation of the magnetic well significantly affects the plasma stored energy. This may be related to the observed electron density fluctuations, which are consistent with theoretical predictions of pressure‐gradient‐driven resistive interchange turbulence. Measurements of the electric potential with a heavy ion beam probe show positive potential in the core of typical ECH discharges and the presence of a velocity shear layer near the edge.

Recent experiments in the Advanced Toroidal Facility (ATF) torsatron [Plasma Physics and Controlled Nuclear Fusion Research 1990 (IAEA, Vienna, in press)] have emphasized the role of magnetic configuration control in transport studies. Long‐pulse plasma operation up to 20 sec has been achieved with electron cyclotron heating (ECH). With neutral beam injection (NBI) power of ≥1 MW, global energy confinement times of 30 msec have been obtained with line‐average densities up to 1.3×1020 m−3. The energy confinement and the operational space in ATF are roughly the same as those in tokamaks of similar size and field. The empirical scaling observed is similar to gyro‐reduced Bohm scaling with favorable dependences on density and field offsetting an unfavorable power dependence. The toroidal current measured during ECH is identified as the bootstrap current. The observed currents agree well with predictions of neoclassical theory in magnitude and in parametric dependence. Variations of the magnetic configuration ...

Numerically calculated tokamak equilibria are used to compute banana‐plateau transport coefficients for finite‐aspect‐ratio, finite‐beta plasmas. Calculations are presented for the Spherical Torus Experiment (STX) (NTIS Document No. DE 86004663) and the Princeton Beta Experiment (PBX) (NTIS Document No. DE 86011173). In STX, the poloidal variation of B≡‖B‖ over a magnetic surface tends to be reduced in regions of large major radius R. The reduction of radial transport caused by this quasiomnigeneous condition is offset by increased drifts and trapping probabilities for smaller R. Thus the modulation Δ=(Bmax−Bmin)/(Bmax+Bmin) on a magnetic surface becomes the critical parameter determining neoclassical transport. In PBX, the bean‐shaped topology of the magnetic surfaces leads to the presence of multiple magnetic wells. Numerical calculations confirm that analytic calculations of neoclassical transport based on the total fraction of circulating particles are valid even when geometrically distinct classes of...