[en] Recent stellarator optimization efforts have primarily targeted transport measures such as quasi-symmetry, effective ripple and alignment of particle guiding center orbits with flux surfaces. For the three forms of quasi-symmetry (helical/toroidal/poloidal), as well as for a variety of nearly-omnigenous systems, this has led to significant reductions in neoclassical losses so that, at least for near-term experiments, the neoclassical transport of particles and energy can be made insignificant compared to anomalous transport. However, momentum transport properties provide an additional dimension for characterizing optimized stellarators. The momentum and flow damping features of optimized stellarators can vary widely, depending on their magnetic structure, ranging from systems with near tokamak-like properties where toroidal flows dominate to those in which poloidal flows dominate and toroidal flows are suppressed. A set of tools has been developed for self-consistently evaluating the flow characteristics of different types of stellarators. Application of this model to existing and planned devices indicates that plasma flow properties vary signicantly. Comparisons across devices can aid in unfolding the interplay between anomalous and neoclassical damping effects as well as the impact of momentum transport properties on related plasma phenomena. (Author)

[en] Proper orthogonal decomposition techniques to reduce noise in the reconstruction of the distribution function in particle-based transport calculations are explored. For two-dimensional steady-state problems, the method is based on low rank truncations of the singular value decomposition of a coarse-grained representation of the particle distribution function. For time-dependent two-dimensional problems or three-dimensional time-independent problems, the use of a generalized low-rank approximation of matrices technique is proposed. The methods are illustrated and tested with Monte Carlo particle simulation data of plasma collisional relaxation and guiding-center transport with collisions in a magnetically confined plasma in toroidal geometry. It is observed that the proposed noise reduction methods achieve high levels of smoothness in the particle distribution function by using significantly fewer particles in the computations.

[en] Energetic particle populations in magnetic confinement systems are sensitive to symmetry-breaking effects due to their low collisionality and long confined path lengths. Broken symmetry is present to some extent in all toroidal devices. As such effects preclude the existence of an ignorable coordinate, a fully three-dimensional analysis is necessary, beginning with the lowest order (equilibrium) magnetic fields. Three-dimensional techniques that have been extensively developed for stellarator configurations are readily adapted to other devices such as rippled tokamaks and helical states in reversed field pinches. This paper will describe the methods and present an overview of recent examples that use these techniques for the modeling of energetic particle confinement, Alfven mode structure and fast ion instabilities.

[en] The internal structure of the toroidicity-induced Alfven eigenmode (TAE) is studied by comparing soft x-ray profile and beam ion loss data taken during TAE activity in the DIII-D tokamak [W. W. Heidbrink , Nucl. Fusion 37, 1411 (1997)] with predictions from theories based on ideal magnetohydrodynamic (MHD), gyrofluid, and gyrokinetic models. The soft x-ray measurements indicate a centrally peaked eigenfunction, a feature which is closest to the gyrokinetic model's prediction. The beam ion losses are simulated using a guiding center code. In the simulations, the TAE eigenfunction calculated using the ideal MHD model acts as a perturbation to the equilibrium field. The predicted beam ion losses are an order of magnitude less than the observed ∼6%--8% losses at the peak experimental amplitude of {delta}B_r/B₀≅2--5 x 10^-4

[en] The shear Alfven spectrum in three-dimensional configurations, such as stellarators and rippled tokamaks, is more densely populated due to the larger number of mode couplings caused by the variation in the magnetic field in the toroidal dimension. This implies more significant computational requirements that can rapidly become prohibitive as more resolution is requested. Alfven eigenfrequencies and mode structures are a primary point of contact between theory and experiment. A new algorithm based on the Jacobi-Davidson method is developed here and applied for a reduced magnetohydrodynamics model to several stellarator configurations. This technique focuses on finding a subset of eigenmodes clustered about a specified input frequency. This approach can be especially useful in modeling experimental observations, where the mode frequency can generally be measured with good accuracy and several different simultaneous frequency lines may be of interest. For cases considered in this paper, it can be a factor of 10²-10³ times faster than more conventional methods.

[en] In the helically-symmetric experiment (HSX) stellarator device, the plasma is both produced and heated by use of electron cyclotron resonance heating (ECRH) at the 2''nd harmonic X-mode resonance. This heating configuration generates a nonthermal energetic electron population. The HSX device is the first of a new generation of stellarators that exploit the concept of quasi-symmetric magnetic fields. Herein, we report on the first experimental evidence of fast-electron-driven Global Alfven Eigenmode (GAE). This mode has previously been observed in both tokamaks and stellarators but it was always driven by energetic ions, not electrons. This instability is observed for quasi-helically symmetric HSX plasmas. Measurements presented in this paper provide two new results; (1) fast electrons can drive the GAE instability, and (2) quasi-symmetry makes a difference by better confining the particles that drive the instability as compared to the conventional stellarator configuration. We report on several features of this fluctuation. It is a coherent, m=1 mode that exhibits both electromagnetic and electrostatic components that are directly measured in the plasma core and edge. Magnetic field fluctuations are measured using external Mirnov coils while interferometry and langmuir probes diagnostics are employed to measure perturbations in the plasma electron density and potential. Fluctuations are observed in the frequency range of 20-120 kHz and scale with ion density and mass according to expectations for Alfvenic modes. The mode is observed to be global and is present in quasi helically symmetric HSX plasma. When quasi-helical symmetry is broken, fast electron confinement deteriorates and the mode is no longer observed. Theory predicts a GAE mode in the gap below the Alfven continua can be excited in the frequency range of the measured fluctuations. By employing a biased electrode inserted into the plasma, flows can be generated. Under these conditions, the Alfvenic mode amplitude is increased and the fluctuations is even observed in the conventional stellarator configuration. The relation between mode amplitude, flows and growth rates will be explored. Supported by U. S. D. O. E. (Author)

[en] The Prototype Material Plasma Exposure eXperiment (Proto-MPEX) is a linear plasma device located at Oak Ridge National Laboratory to develop the plasma source concept for the Materials Plasma Exposure eXperiment (MPEX). Recent experiments have demonstrated the heating of electrons in a high-density deuterium plasma ($n_e\sim <!--\; ???\; -->5\times <!--\; ??\; -->{10}^{19}{\mathrm{m}}^{-<!--\; ???\; -->3}$) via electron Bernstein waves and source plasma production via helicon waves in this linear configuration. Moreover, experimental observations suggest that the magnetic ripple adversely affects the parallel transport of the heated electrons toward the target where material samples are to be exposed to the plasma. To understand the transport process during microwave application, a test-particle Monte-Carlo (MC) code has been developed that incorporates the effects of Coulomb collisions, magnetic mirror adiabatic trapping and electron cyclotron interaction via a quasilinear RF heating operator. MC calculations indicate that the absence of 2nd turning points along the trajectory of cyclotron heated electrons significantly reduces adiabatic trapping and maximizes power transport to the Target surface. Thermalization of cyclotron heating electrons is analyzed with the MC code and it is found that for conditions relevant to Proto-MPEX, a significant fraction of the absorbed heating power is coupled to the Target surface via ballistic fast electrons; however, under certain conditions, up to 60% of the absorbed RF power can be dissipated via thermalization of the fast electrons on the background plasma. Results are compared with experimental measurements. Finally, the implications of the results are discussed in the context of the upcoming MPEX device. (paper)

[en] Comprehensive understanding of energetic-ion-driven global instabilities such as Alfven eigenmodes (AEs) and their impact on energetic ions and bulk plasma is crucially important for tokamak and stellarator/helical plasmas and in the future for deuterium-tritium (DT) burning plasma experiments. Various types of global modes and their associated enhanced energetic ion transport are commonly observed in toroidal plasmas. Toroidicity-induced AEs and ellipticity-induced AEs, whose gaps are generated through poloidal mode coupling, are observed in both tokamak and stellarator/helical plasmas. Global AEs and reversed shear AEs, where toroidal couplings are not as dominant were also observed in those plasmas. Helicity induced AEs that exist only in 3D plasmas are observed in the large helical device (LHD) and Wendelstein 7 Advanced Stellarator plasmas. In addition, the geodesic acoustic mode that comes from plasma compressibility is destabilized by energetic ions in both tokamak and LHD plasmas. Nonlinear interaction of these modes and their influence on the confinement of the bulk plasma as well as energetic ions are observed in both plasmas. In this paper, the similarities and differences in these instabilities and their consequences for tokamak and stellarator/helical plasmas are summarized through comparison with the data sets obtained in LHD. In particular, this paper focuses on the differences caused by the rotational transform profile and the 2D or 3D geometrical structure of the plasma equilibrium. Important issues left for future study are listed.

[en] The modification of the shear Alfvén spectrum due to a core resonant magnetic island is used to explain the Alfvénic activity observed on the Madison symmetric torus (MST) reversed-field pinch during neutral beam injection. Theoretical studies show that the Alfvén continua in the core of the island provide a gap in which the observed Alfvénic bursts reside. Numerical simulations using a new code called SIESTAlfvén have identified the bursts as the first observation of an island-induced Alfvén eigenmode (IAE) in an RFP. The IAE arises from a helical coupling of harmonics due to the magnetic island. (paper)

[en] Observations on the National Spherical Torus eXperiment (NSTX) indicate that externally applied non-axisymmetric magnetic perturbations (MP) can reduce the amplitude of Toroidal Alfven Eigenmodes (TAE) and Global Alfven Eigenmodes (GAE) in response to pulsed n=3 non-resonant fields. From full-orbit following Monte Carlo simulations with the 1- and 2-fluid resistive MHD plasma response to the magnetic perturbation included, it was found that in response to MP pulses the fast-ion losses increased and the fast-ion drive for the GAEs was reduced. The MP did not affect the fast-ion drive for the TAEs significantly but the Alfven continuum at the plasma edge was found to be altered due to the toroidal symmetry breaking which leads to coupling of different toroidal harmonics. The TAE gap was reduced at the edge creating enhanced continuum damping of the global TAEs, which is consistent with the observations. Furthermore, the results suggest that optimized non-axisymmetric MP might be exploited to control and mitigate Alfven instabilities by tailoring the fast-ion distribution function and/or continuum structure