WAVE-PARTICLE INTERACTIONS AND PLASMA FUELING RESEARCH

The following provides a summary of the recent research interests in wave particle interactions and plasma fueling of the GA Theory Group. The descriptions of work in both of these areas are intended to provide some motivation and background as well as a summary of some of the more important contributions of the group. References are provided at the end.

ICRF Wave-Plasma Interactions: Experiments from many tokamaks (JT-60U, JET, TEXTOR and DIII-D) [Pinsker 1999, Petty 1997, Petty 2001] and spherical tori (NSTX) [Rosenberg 2003] show significant interactions between high harmonic ICRF waves (n ³ 2) and neutral-beam (NB) injected ion species. As a result of the interactions, non-Maxwellian beam-ion distributions with high energy tails above the injected beam energy are generated, which can lead to enhanced neutron production in the experiments. DIII-D experiments also show that power absorption by energetic ions may significantly reduce the fast wave current drive (FWCD) and its efficiency [Petty 1997]. Conventional simulations based on Fokker-Planck codes do not include finite ion-orbit effects and, therefore, cannot fully explain these experimental observations. In a large burning-device like ITER, a large population of energetic ions exists in the form of injected NB ions and fusion-born alphas, and it is particularly important to self-consistently include the RF-generated orbit effects.

The drift-orbit RF code ORBIT-RF was previously developed to model ICRF-driven plasma rotation in tokamaks [Chan 2002], ORBIT-RF solves the Hamiltonian guiding center drift equations to follow trajectories of energetic ions in 2D magnetic equilibrium under Coulomb collisions and ICRF quasi-linear heating. An RF-induced random walk model is used to replicate quasi-linear diffusion. The generalized high harmonic RF diffusion operator is included to calculate perpendicular RF-kicks including Doppler shifts. The study indicates that ICRF induced energetic tails may play a role in the generation of plasma rotation that has beneficial effects on tokamak confinement and stability. This is due to the generation of a net J�B torque that produces sheared toroidal rotation from radial currents generated by the non-ambipolar RF-induced transport of energetic tails [Chan 2002].

Significant progress has been made recently in the development and application of ORBIT-RF to model interactions of ICRF waves with plasmas [Choi 2003a]. A mono-energetic NB slowing down model was added to ORBIT-RF. The NB-injected fast ions are modeled as a test particle source. The steady state slowing down distribution of the beam ion species is then computed using a re-injection method to replenish the thermalized beam ions. The magnitude of the ICRF wave field and its perpendicular wave number are calculated based on the Stix cold plasma model with an assumed parabolic radial dependence.

Some preliminary simulations of a DIII-D FWCD discharge have been performed to explore the interactions between the deuterium beam ions and the ICRF wave at the 4th harmonic resonance near the magnetic axis [Choi 2003b]. Energetic tails up to several hundred keV are produced when the ICRF wave is turned on and the beam-ion energy spectrum is broadened due to the finite-orbit effect of energetic ions. As shown in the figure above, the calculated neutron enhancement factor first varies slowly with |E+| then strongly when |E+| > 1400 V/m. The simulation with |E+| ~ 1900 V/m, estimated from the Stix model results in a neutron enhancement factor ~ 2 times higher than the experimental one. Several factors may contribute to this discrepancy. First, the simplified |E+| profile used in the calculations may not be sufficiently accurate. Indeed, as shown in the diagram above, on the right, the wave fields computed more realistically using the full wave code TORIC vary much more rapidly across the resonant layer near the magnetic axis than those given by the parabolic radial dependence used in these calculations. Secondly, in these calculations energetic ion losses due to charge exchange and interception by the surrounding vacuum vessel are ignored. These can lead to non-negligible modifications of the fast ion distribution. Furthermore, the non-ambipolar radial transport due to ICRF minority heating is expected to modify the radial electric field, which could have additional effects on the fast ion distribution.

Pellet ablation and Cloudlet Drift Studies: Achieving high plasma densities, under long pulse or steady state conditions, with favorable confinement, is critical for meeting fusion power performance requirements in next-step devices such as ITER. Fueling by pellet injection, which can produce deposition deep inside the plasma, will play a vital role in the proposed burning plasma experiments. A key aim of pellet ablation research is to predict the plasma profiles just after pellet injection. The physical processes governing pellet ablation and ionization differ from the subsequent advection and distribution of the ionized material within the plasma column. In the process of ablation, driven by the plasma electron heat flux, a strongly localized, high-pressure plasmoid forms around the pellet on a fast time scale. Owing to the 1/R toroidal magnetic field inhomogeneity, a �B and curvature drift current is induced inside the plasmoid. This gives rise to a time-dependent vertical E-field inside, which accelerates the plasmoid at the E�B drift velocity in the large-R direction [Parks 2000]. The presence of a plasmoid moving across the magnetic field is communicated to the other parts of the torus by the propagation of Alfven waves along the field lines. For high-field-side (HFS) pellet injection, this drift is inward and allows the pellet ablation material to penetrate rather deeply into the hot plasma, well beyond the point where the solid pellet burns out.

Two computational tools, CAP (Code of Ablation Process) [Ishizaki and Parks 2004] and PRL (Pressure Relaxation Lagrangian Code) [Parks 2000] have been developed to model these processes as two separate pellet ablation and pellet cloud advection phases, respectively. CAP is a 2D (r, z) time-dependent hydrodynamic code. It is used to model the first pellet ablation phase from the inner cold and dense radially symmetric flow region to the outer ionized field-aligned region. Unique CAP features include a capability to handle the steep density and temperature gradients near the pellet surface (deflagration front) and at a shock front. It can also treat the nebulous boundary layer where the solid undergoes transformation to a gas and the pellet surface recedes. The parameters of the field aligned-flow region will serve as initial conditions for the numerical simulation of mass relocation and deposition described by the PRL code.

The PRL Code solves the vorticity equation describing the cross-field incompressible flows associated with the coherent E�B drift motion of the cigar-shaped cloudlet while it is elongating parallel to B. The cloud pressure reaches equilibrium with the background pressure after a few sound times where and are the initial cloud half-length and transverse radius. The additional curvature drift induced by parallel flow in the curved B-field maintains E�B drift, even after the pressure equilibrates, and thus significantly enhances the penetration depth.

Fundamentally new advances have been made recently that significantly improve the understanding of the pellet fueling physics as well as the computation capability of the two pellet modeling tools CAP and PRL. In particular, a CAP simulation of pellet ablation carried out in collaboration with Ishizaki from NIFS indicates that ionization causes the formation of a stationary shock front in the supersonic region of the ablation flow that is followed by a �second� sonic surface farther out, as previously conjectured. Anisotropic heating caused by the directionality of the magnetic field also leads to a non-uniform pressure distribution over the pellet surface. Because the pellet behaves almost as a hydraulic fluid under high shear stress, it can deform into a pancake shape, flattened in the direction of the magnetic field, and elongated in the perpendicular direction, as was also previously conjectured. Such 2D deformations can significantly cut the pellet lifetime. Secondly, a new form of the parallel vorticity equation in a special field line following coordinate system was used to solve for the E�B pellet cloud drift and mass deposition profile in toroidal geometry. Favorable agreement with the experimental profile following HFS pellet injection into DIII�D was found. This is illustrated in the figure below (left); the right hand figure shows a preliminary simulation for the projected Dne profile in ITER. The prospects for deep fueling in ITER look encouraging.

So far, the treatment of the 2D transition from the inner radially nearly symmetric flow to the outer magnetic field aligned region in the CAP code is incomplete. The magnetic J�B magnetic force is neglected in the force balance. This can have a significant effect on the pellet ablation. Also, magnetic shear effects have been neglected in the PRL code. This can result in a differential drift that shortens the drift distance and significantly spread out the fuel deposition profile.

High-density gas jet fuelling is also being considered. Unlike pellet, high-density gas jet can provide a method that fuels the plasma continuously rather than perturbatively. This may be important for ITER, as it would avoid generation of neoclassical tearing modes and confinement degradation often seen in current pellet experiments above a certain power threshold [Maigni 1997, Lang 2000].