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In this paper, a similarity relation between RF wave systems in tokamaks is found theoretically by investigating scaling conditions of plasma density and temperature, tokamak size and background magnetic fields, and RF wave frequency and power. The scaling conditions simultaneously satisfy Maxwell's equations, the Grad-Shafranov equation, and the Fokker-Planck equation. The consistency of the scaling with transport equations is examined by several empirical and theoretical scalings for confinement time. The similarity found in this paper is useful to investigate the possibility of the test system for RF wave experiments and verify the coupled numerical codes for the wave modeling.In this paper, a similarity relation between RF wave systems in tokamaks is found theoretically by investigating scaling conditions of plasma density and temperature, tokamak size and background magnetic fields, and RF wave frequency and power. The scaling conditions simultaneously satisfy Maxwell's equations, the Grad-Shafranov equation, and the Fokker-Planck equation. The consistency of the scaling with transport equations is examined by several empirical and theoretical scalings for confinement time. The similarity found in this paper is useful to investigate the possibility of the test system for RF wave experiments and verify the coupled numerical codes for the wave modeling.

Nonlinear rf-driven sheared flows are of interest for turbulence control and basic physics experiments. Short-wavelength slow modes are required for efficient coupling of wave momentum to the plasma, requiring a kinetic hot-plasma theory. Here, a guiding-center formulation is developed which calculates the nonlinear particle and energy fluxes, energy absorption, and nonlinear forces on the plasma using a kinetic moment approach that is valid to first order in the ratio of the gyroradius compared to the wave envelope scale length and the plasma equilibrium scale length. Both the stress tensor and Lorentz force contribute to the net force on a fluid element. The forces driving flux-surface-averaged flows in a tokamak are extracted from the parallel and toroidal components. It is shown that flux-surface-averaged flows are driven by two classes of terms: direct absorption of wave momentum and dissipative stresses. Furthermore, the general kinetic expression for the force is shown to reduce to the standard cold-fluid ponderomotive force in an appropriate limit, but in this limit no flows are driven.

Fast wave (FW) studies of mode conversion (MC) processes at the ion–ion hybrid layer in toroidal plasmas must capture the disparate scales of the FW and mode converted ion Bernstein and ion cyclotron waves. Correct modeling of the MC layer requires resolving wavelengths on the order of k⊥ρi∼1 which leads to a scaling of the maximum poloidal mode number, Mmax, proportional to 1/ρ* (ρ*≡ρi/L). The computational resources needed scale with the number of radial (Nr), poloidal (Nθ), and toroidal (Nφ) elements as Nr * Nφ * Nθ3. Two full wave codes, a massively-parallel-processor (MPP) version of the TORIC-2D finite Larmor radius code [M. Brambilla, Plasma Phys. Controlled Fusion 41, 1 (1999)] and also an all orders spectral code AORSA2D [E. F. Jaeger et al., Phys. Plasmas 9, 1873 (2002)], have been developed which for the first time are capable of achieving the resolution and speed necessary to address mode conversion phenomena in full two-dimensional (2-D) toroidal geometry. These codes have been used in conjunction with theory and experimental data from the Alcator C-Mod [I. H. Hutchinson et al., Phys. Plasmas 1, 1511 (1994)] to gain new understanding into the nature of FWMC in tokamaks. The massively-parallel-processor version of TORIC is also now capable of running with sufficient resolution to model planned lower hybrid range of frequencies experiments in the Alcator C-Mod.

Ion absorption of the high harmonic fast wave in a spherical torus [Y.-K. M. Peng et al., Nucl. Fusion 26, 769 (1986)] is of critical importance to assessing the viability of the wave as a means of heating and driving current. Analysis of recent National Spherical Torus Experiment [M. Ono et al., Nucl. Fusion 40, 557 (2000)] shots has revealed that under some conditions when neutral beam and rf power are injected into the plasma simultaneously, a fast ion population with energy above the beam injection energy is sustained by the wave. In agreement with modeling, these experiments find the rf-induced fast ion tail strength and neutron rate at lower B-fields to be less enhanced, likely due to a larger β profile, which promotes greater off-axis absorption where the fast ion population is small. Ion loss codes find the increased loss fraction with decreased B insufficient to account for the changes in tail strength, providing further evidence that this is a rf interaction effect. Though greater ion absorption...

The ability to obtain high plasma densities with high fractional ionization using readily available, low-cost components makes the helicon a candidate plasma source for many applications, including plasma rocket propulsion, fusion component testing, and materials processing. However, operation of a helicon can be a sensitive function of the magnetic field strength and geometry as well as the driving frequency, especially when using light feedstock gases such as hydrogen or helium. In this paper, results from a coupled rf and transport model are compared with experiments in the axially inhomogeneous Mini-Radio Frequency Test Facility [Goulding et al., Proceedings of the International Conference on Electromagnetics in Advanced Applications (ICEAA 99), Torino, Italy, 1999 (Litografia Geda, Torino, 1999), p. 107] (Mini-RFTF). Experimental observations of the radial shape of the density profile can be quantitatively reproduced by iteratively converging a high-resolution rf calculation including the rf parallel electric field with a transport model using reasonable choices for the transport parameters. The experimentally observed transition into the high density helicon mode is observed in the model, appearing as a nonlinear synergism between radial diffusion, the rf coupling to parallel electric fields that damp near the plasma edge, and propagation of helicon waves that collisionally damp near the axis of the device. Power deposition from various electric field components indicates that inductive coupling and absorption in the edge region can reduce the efficiency for high-density operation. The effects of absorption near the lower hybrid resonance in the near-field region of the antenna are discussed. Ponderomotive effects are also examined and found to be significant only in very low density and edge regions of the Mini-RFTF discharge.

Previous full-wave models for rf heating in multidimensional plasmas have relied on either cold-plasma or finite Larmor radius approximations. These models assume that the perpendicular wavelength of the rf field is much larger than the ion Larmor radius, and they are therefore limited to relatively long wavelengths and low cyclotron harmonics. Recently, alternate full-wave models have been developed that eliminate these restrictions. These “all orders spectral algorithms” take advantage of new computational techniques for massively parallel computers to solve the integral form of the wave equation in multiple dimensions without any restriction on wavelength relative to orbit size, and with no limit on the number of cyclotron harmonics retained. These new models give high-resolution, two-dimensional solutions for mode conversion and high harmonic fast wave heating in tokamak geometry. In addition, they have been extended to give fully three-dimensional solutions of the integral wave equation for minority ion cyclotron heating in stellarator geometry. By combining multiple periodic solutions for individual helical field periods, it is possible to obtain complete wave solutions valid over the entire volume of the stellarator for arbitrary antenna geometry.

In this paper, a reduced model of quasilinear diffusion by a small Larmor radius approximation is derived to couple the Maxwell's equations and the Fokker-Planck equation self-consistently for ion cyclotron range of frequency waves in a tokamak. The reduced model ensures the important properties of the full model by Kennel-Engelmann diffusion, such as diffusion directions, wave polarizations, and H-theorem. The kinetic energy change (W-dot) is used to derive the reduced model diffusion coefficients for the fundamental damping and the second harmonic damping to the lowest order of the finite Larmor radius expansion. The quasilinear diffusion coefficients are implemented in a coupled code (TORIC-CQL3D) with the equivalent reduced model of dielectric tensor. We also present the simulations of the ITER minority heating scenario, in which the reduced model is verified within the allowable errors from the full model results., 26 pages, 6 figures

Spectral calculations of radio-frequency (rf) heating in tokamak plasmas are extended to two dimensions (2-D) by taking advantage of new computational tools for distributed memory, parallel computers. The integral form of the wave equation is solved in 2-D without any assumption regarding the smallness of the ion Larmor radius (ρ) relative to the perpendicular wavelength (λ⊥). Results are therefore applicable to all orders in k⊥ρ, where k⊥=2π/λ⊥. Previous calculations of rf wave propagation and heating in 2-D magnetized plasmas have relied on finite Larmor radius expansions (k⊥ρ≪1) and are thus limited to relatively long wavelengths. In this paper, no such assumption is made, and we consider short wavelength processes such as the excitation and absorption of ion Bernstein waves in 2-D with k⊥ρ>1. Results show that this phenomenon is far more complex than simple one-dimensional plasma models would suggest. Other applications include fully self-consistent 2-D solutions for high-harmonic fast-wave heating in...

A full-wave, one-dimensional spectral model is developed to study sheared poloidal flow driven by high-harmonic ion Bernstein waves (IBWs) in tokamak plasmas. The local plasma conductivity is corrected to lowest order in ρ/L where ρ is the ion Larmor radius and L is the equilibrium scale length. This correction takes into account gradients in equilibrium quantities and is necessary for conservation of energy. It is equivalent to the “odd-order derivative” terms in finite difference models. No assumption is made regarding the smallness of the ion Larmor radius relative to wavelength, and results are applicable to all orders in k⊥ρ where k⊥ is the perpendicular wave number. Previous numerical results for flow drive have relied on expansions in k⊥ρ, and are thus limited to cyclotron harmonics of two and below. In this article, we consider higher-harmonic cases corresponding to recent IBW flow drive experiments on the Tokamak Fusion Test Reactor [B. P. LeBlanc, R. E. Bell, S. Bernabei et al., Phys. Rev. Lett....

Because alpha particle losses can have a significant influence on tokamak reactor viability, the loss of deuterium–tritium alpha particles from the Tokamak Fusion Test Reactor (TFTR) [K. M. McGuire et al., Phys. Plasmas 2, 2176 (1995)] has been measured under a wide range of conditions. In TFTR, first orbit loss and stochastic toroidal field ripple diffusion are always present. Other losses can arise due to magnetohydrodynamic instabilities or due to waves in the ion cyclotron range of frequencies. No alpha particle losses have yet been seen due to collective instabilities driven by alphas. Ion Bernstein waves can drive large losses of fast ions from TFTR, and details of those losses support one element of the alpha energy channeling scenario.

Radio frequency wave propagation in finite temperature, magnetized plasmas exhibits a wide range of physics phenomena. The plasma response is nonlocal in space and time, and numerous modes are possible with the potential for mode conversions and transformations. In addition, diffraction effects are important due to finite wavelength and finite-size wave launchers. Multidimensional simulations are required to describe these phenomena, but even with this complexity, the fundamental plasma response is assumed to be the uniform plasma response with the assumption that the local plasma current for a Fourier mode can be described by the “Stix” conductivity. However, for plasmas with non-uniform magnetic fields, the wave vector itself is nonlocal. When resolved into components perpendicular (k⊥) and parallel (k||) to the magnetic field, locality of the parallel component can easily be violated when the wavelength is large. The impact of this inconsistency is that estimates of the wave damping can be incorrect (t...

The Alfven resonances may occur on the low- and high-field sides for a low-frequency fast wave current drive scenario proposed for the International Thermonuclear Experimental Reactor (ITER) [Nucl. Fusion 31, 1135 (1991)]. At the resonance on the low-field side, the fast wave may be mode converted into a short-wavelength slow wave, which can be absorbed by electrons at the plasma edge, before the fast wave propagates into the core area of the plasma. Such absorption may cause a significant parasitic power loss.

The first experiments utilizing high‐power radio waves in the ion cyclotron range of frequencies to heat deuterium–tritium (D–T) plasmas have been completed on the Tokamak Fusion Test Reactor [Fusion Technol. 21, 13 (1992)]. Results from the initial series of experiments have demonstrated efficient core second harmonic tritium (2ΩT) heating in parameter regimes approaching those anticipated for the International Thermonuclear Experimental Reactor [D. E. Post, Plasma Physics and Controlled Nuclear Fusion Research, Proceedings of the 13th International Conference, Washington, DC, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 239]. Observations are consistent with modeling predictions for these plasmas. Efficient electron heating via mode conversion of fast waves to ion Bernstein waves has been observed in D–T, deuterium‐deuterium (D–D), and deuterium–helium‐4 (D–4He) plasmas with high concentrations of minority helium‐3 (3He) (n3He/ne≳10%). Mode conversion current drive in D–T plasmas ...

A new mechanism is identified for radio frequency (RF) wave induced force and current drive caused by a kinetic flux carried by coherent oscillations of plasma particles. The induced force along a magnetic field line by RF heating of plasmas is calculated with a one‐dimensional slab model, and found to be contributed by the plasma power absorption and spatial inhomogeneity. The inhomogeneity term consists of a kinetic flux and a flux related to RF wave helicity injection rate. The effect from the kinetic flux exists only in a warm plasma, whereas, in contrast, the effect from the helicity related flux exists even in a cold plasma. The forces are calculated for both electrons and ions in the ion cyclotron range of frequencies (ICRF), and the effects from the ion cyclotron and the second harmonic resonance are included.

Fast wave poloidal flow generation at the plasma edge of a tokamak is studied with a one‐dimensional slab model. In the absence of mode conversion, the poloidal flow can be generated by a spatial change of plasma velocity and current density profiles due to strong minority ion power absorption at the minority ion cyclotron resonance. The electromagnetic force plays a more important role in the flow generation than does the plasma Reynolds stress. In the presence of mode conversion, the flow is mainly generated by interference between the long‐wavelength transmitted fast wave and the short‐wavelength ion Bernstein wave (IBW) from mode conversion. Flow shear generated in the presence of mode conversion varies spatially with a scale length similar to the IBW wavelength. With mode conversion, the plasma Reynolds stress becomes more important in the flow shear generation than the electromagnetic force. For both cases, the plasma Reynolds stress and the electromagnetic force are out of phase, so that the result...

The final hardware modifications for tritium operation have been completed for the Tokamak Fusion Test Reactor (TFTR) [Fusion Technol. 21, 1324 (1992)]. These activities include preparation of the tritium gas handling system, installation of additional neutron shielding, conversion of the toroidal field coil cooling system from water to a FluorinertTM system, modification of the vacuum system to handle tritium, preparation, and testing of the neutral beam system for tritium operation and a final deuterium–deuterium (D–D) run to simulate expected deuterium–tritium (D–T) operation. Testing of the tritium system with low concentration tritium has successfully begun. Simulation of trace and high power D–T experiments using D–D have been performed. The physics objectives of D–T operation are production of ≊10 MW of fusion power, evaluation of confinement, and heating in deuterium–tritium plasmas, evaluation of α‐particle heating of electrons, and collective effects driven by alpha particles and testing of diag...

Profiles of the noninductive current, driven by direct electron absorption of fast waves in the ion cyclotron range of frequencies, have been determined for DIII‐D tokamak discharges [Luxon et al., Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159]. The results clearly indicate the presence of centrally peaked driven current and validate theoretical models of fast wave current drive.

Spurious resonances exist in the dispersion relations for finite Larmor radius models in plasma heating in the ion cyclotron range of frequencies. The spurious resonances occur when the highest‐order coefficient in a fourth‐order equation vanishes. It is shown that the spurious resonances cannot be removed by using a sixth‐order equation because the highest‐order coefficient in the sixth‐order equation also vanishes at the same location as the highest‐order coefficient in the fourth‐order equation. However, the spurious modes are often not excited when solving the corresponding ordinary differential equations (ODEs) for an incident fast wave so that the solutions from the ODEs are often accurate.

Radio frequency waves in the ion cyclotron range of frequencies (ICRF) are widely used to heat tokamak plasmas. In ICRF heating schemes involving multiple ion species, the launched fast waves convert to ion cyclotron waves or ion Bernstein waves at the two-ion hybrid resonances. Mode converted waves are of interest as actuators to optimise plasma performance through current drive and flow drive. In order to describe these processes accurately in a realistic tokamak geometry, numerical simulations are essential, and it is important that these codes be validated against experiment. In this study, the mode converted waves were measured using a phase contrast imaging technique in D-H and D-[superscript 3]He plasmas. The measured mode converted wave intensity in the D-[superscript 3]He mode conversion regime was found to be a factor of ∼ 50 weaker than the full-wave predictions. The discrepancy was reduced in the hydrogen minority heating regime, where mode conversion is weaker., United States. Dept. of Energy (DE-FG02-94-ER54235), United States. Dept. of Energy (DE-FC02-99-ER54512), United States. Dept. of Energy (DE-FC02-01ER54648)

The five-dimensional finite-orbit Monte Carlo code ORBIT-RF [M. Choi et al., Phys. Plasmas 12, 1 (2005)] is successfully coupled with the two-dimensional full-wave code all-orders spectral algorithm (AORSA) [E. F. Jaeger et al., Phys. Plasmas 13, 056101 (2006)] in a self-consistent way to achieve improved predictive modeling for ion cyclotron resonance frequency (ICRF) wave heating experiments in present fusion devices and future ITER [R. Aymar et al., Nucl. Fusion 41, 1301 (2001)]. The ORBIT-RF/AORSA simulations reproduce fast-ion spectra and spatial profiles qualitatively consistent with fast ion D-alpha [W. W. Heidbrink et al., Plasma Phys. Controlled Fusion 49, 1457 (2007)] spectroscopic data in both DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] and National Spherical Torus Experiment [M. Ono et al., Nucl. Fusion 41, 1435 (2001)] high harmonic ICRF heating experiments. This work verifies that both finite-orbit width effect of fast-ion due to its drift motion along the torus and iterations between fast-ion distribution and wave fields are important in modeling ICRF heating experiments.

To fully account for the wave-particle interaction physics in ion cyclotron resonant frequency (ICRF) heating experiment, finite orbit effects and non-Maxwellian distribution have to be self-consistently coupled with full-wave solutions. For this purpose, the five-dimensional Monte Carlo code ORBIT-RF [M. Choi et al., Phys. Plasmas 12, 1 (2005)] is being coupled with the two-dimensional full-wave code AORSA [E. F. Jaeger et al., Phys. Plasmas 13, 056101 (2006)] to iteratively evolve the ion distribution in four-dimensional spatial velocity space that is used to update the dielectric tensor in AORSA for evaluating the full-wave fields. In this paper, it is demonstrated that using the full-wave fields from a Maxwellian dielectric tensor in AORSA and confining the resonant ions to their initial orbits in ORBIT-RF, ORBIT-RF largely reproduces the AORSA linear wave absorption profiles for fundamental and higher harmonic ICRF heating. An exception is an observed inward shift in the ORBIT-RF absorption peak for ...

The problem of “far-field” sheath formation is studied with a new quantitative one-dimensional model. These radio-frequency (rf) sheaths occur when unabsorbed fast waves in the ion cyclotron range of frequencies are incident on a conducting surface not aligned with a flux surface. Use of a nonlinear sheath boundary condition gives self-consistent solutions for the wave fields and sheath characteristics, and it introduces a sheath-plasma-wave resonance which can enhance the sheath potential. The model is used to compute the parametric dependence of the far-field sheath potential. Its application to post-process the rf fields computed by a full-wave code for a typical D(H) minority heating scenario is also discussed. This work shows that two-dimensional effects (included heuristically) are essential in determining whether far-field sheath potentials are strong enough to cause significant edge interactions, such as impurity generation and reduced heating efficiency.

The next step toward fusion as a practical energy source is the design and construction of ITER [R. Aymar et al., Nucl. Fusion 41, 1301 (2001)], a device capable of producing and controlling the high-performance plasma required for self-sustaining fusion reactions, i.e., “burning plasma.” ITER relies in part on ion-cyclotron radio frequency power to heat the deuterium and tritium fuel to fusion temperatures. In order to heat effectively, the radio frequency wave fields must couple efficiently to the dense core plasma. Calculations in this paper support the argument that this will be the case. Three-dimensional full-wave simulations show that fast magnetosonic waves in ITER propagate radially inward with strong central focusing and little toroidal spreading. Energy deposition, current drive, and plasma flow are all highly localized near the plasma center. Very high resolution, two-dimensional calculations reveal the presence of mode conversion layers, where fast waves can be converted to slow ion cyclotron...

High harmonic fast wave heating and current drive (CD) are being developed on the National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 41, 1435 (2001)] for supporting startup and sustainment of the ST plasma. Considerable enhancement of the core heating efficiency (η) from 44% to 65% has been obtained for CD phasing of the antenna (strap-to-strap φ = -90o, kφ = -8 m-1) by increasing the magnetic field from 4.5 kG to 5.5 kG. This increase in efficiency is strongly correlated to moving the location of the onset density for perpendicular fast wave propagation (nonset ∝ ΒΦ× k|| 2/w) away from the antenna face and wall, and hence reducing the propagating surface wave fields. RF waves propagating close to the wall at lower BΦ and k|| can enhance power losses from both the parametric decay instability (PDI) and wave dissipation in sheaths and structures around the machine. The improved efficiency found here is attributed to a reduction in the latter, as PDI losses are little changed at the higher magnetic field. Under these conditions of higher coupling efficiency, initial measurements of localized CD effects have been made and compared with advanced RF code simulations

Magnetically confined plasmas can contain significant concentrations of nonthermal plasma particles arising from fusion reactions, neutral beam injection, and wave-driven diffusion in velocity space. Initial studies in one-dimensional and experimental results show that nonthermal energetic ions can significantly affect wave propagation and heating in the ion cyclotron range of frequencies. In addition, these ions can absorb power at high harmonics of the cyclotron frequency where conventional two-dimensional global-wave models are not valid. In this work, the all-orders global-wave solver AORSA [E. F. Jaeger et al., Phys. Rev. Lett. 90, 195001 (2003)] is generalized to treat non-Maxwellian velocity distributions. Quasilinear diffusion coefficients are derived directly from the wave fields and used to calculate energetic ion velocity distributions with the CQL3D Fokker-Planck code [R. W. Harvey and M. G. McCoy, Proceedings of the IAEA Technical Committee Meeting on Simulation and Modeling of Thermonuclear ...