E. F. Jaeger

Power deposition in high‐density inductively coupled plasma tools for semiconductor processing

A two‐dimensional, computationally efficient numerical model is developed to study power deposition in high‐density inductively coupled plasma sources. Calculations include both inductive coupling, caused by plasma response to external coil currents, and capacitive coupling, caused by plasma response to external voltages on the coils and wafer. Variation in current along the induction coil is determined self‐consistently from the integral constraint of charge conservation. Sheath phenomena are incorporated through previously published analytic models. The system behavior is analogous in some respects to that of a transmission line. Comparison with measurement suggests that this model provides a good description of self‐consistent coil response when the electric field exhibits less than a quarter wavelength per coil turn.

All-orders spectral calculation of radio-frequency heating in two-dimensional toroidal plasmas

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...

Comparing experiments with modeling for light ion helicon plasma sources

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.

High Harmonic Fast Wave Heating Efficiency Enhancement and Current Drive at Longer Wavelength on the National Spherical Torus Experiment

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

Advances in full-wave modeling of radio frequency heated, multidimensional plasmas

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 ...

Exact and approximate solutions to the finite temperature wave equation in a one-dimensional perpendicularly stratified plasma

The sixth order wave equation which results from a finite temperature expansion of the Vlasov equation is solved globally in the ion cyclotron range of frequencies. A perpendicularly stratified, onedimensional slab plasma is assumed. The diamagnetic drift and the associated anisotropy are included in the unperturbed distribution function to ensure a self-adjoint system. All x-dependence in the plasma pressure and magnetic field is retained along with the electric field parallel to . Thus, Landau damping of the ion Bernstein wave is included self-consistently. Because of the global nature of the solution, the evanescent short wavelength Bernstein waves do not grow exponentially as in shooting methods. Strong variations occur in the absorption and in the structure of the wave fields as resonance topology is varied. Solutions to the complete sixth order differential equation are compared to those from an approximate second order equation based on local dispersion theory.

Self-consistent full-wave and Fokker-Planck calculations for ion cyclotron heating in non-Maxwellian plasmas

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 ...

Full wave simulations of fast wave heating losses in the scrape-off layer of NSTX and NSTX-U

Full wave simulations of fusion plasmas show a direct correlation between the location of the fast-wave cut-off, radiofrequency (RF) field amplitude in the scrape-off layer (SOL) and the RF power losses in the SOL observed in the National Spherical Torus eXperiment (NSTX). In particular, the RF power losses in the SOL increase significantly when the launched waves transition from evanescent to propagating in that region. Subsequently, a large amplitude electric field occurs in the SOL, driving RF power losses when a proxy collisional loss term is added. A 3D reconstruction of absorbed power in the SOL is presented showing agreement with the RF experiments in NSTX. Loss predictions for the future experiment NSTX-Upgrade (NSTX-U) are also obtained and discussed.

Full-wave calculation of sheared poloidal flow driven by high-harmonic ion Bernstein waves in tokamak plasmas

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....

Advances in high-harmonic fast wave physics in the National Spherical Torus Experiment

Improved core high-harmonic fast wave (HHFW) heating at longer wavelengths and during start-up and plasma current ramp-up has now been obtained by lowering the edge density with lithium wall conditioning, thereby moving the critical density for perpendicular fast-wave propagation away from the vessel wall. Lithium conditioning allowed significant HHFW core electron heating of deuterium neutral beam injection (NBI) fuelled H-mode plasmas to be observed for the first time. Large edge localized modes were observed immediately after the termination of rf power. Visible and infrared camera images show that fast wave interactions can deposit considerable rf energy on the outboard divertor. HHFW-generated parametric decay instabilities were observed to heat ions in the plasma edge and may be the cause for a measured drag on edge toroidal rotation during HHFW heating. A significant enhancement in neutron rate and fast-ion profile was measured in NBI-fuelled plasmas when HHFW heating was applied.