Pellet Ablation Rate Research Articles

Influence of a Secondary Plasma Cloud on the Ablation of Pellets in Magnetic Confinement Devices

The analysis of experimental data on the structure of hydrocarbon pellet clouds on the LHD stellarator has allowed one to estimate the relative contributions of neutral and plasma shielding at the ablation of macroparticles (pellets) in a high-temperature magnetized toroidal plasma. A method for the self-consistent calculation of the pellet ablation rate, the characteristic size of the pellet cloud, and the electron density in its singly ionized part including neutral gas and plasma shielding is described. This calculation for polystyrene pellets injected into the LHD plasma gives the results that agree with the experimental data obtained during the early ablation phase, when the ablation rate is determined by thermal electrons and the contribution of the superthermal component of the hot plasma to ablation can be neglected.

Estimate of pre-thermal quench non-thermal electron density profile during Ar pellet shutdowns of low-density target plasmas in DIII-D

The radial density profile of pre-thermal quench (pre-TQ) early-time non-thermal (hot) electrons is estimated by combining electron cyclotron emission and soft x-ray data during the rapid shutdown of low-density (ne≲1019 m−3) DIII-D target plasmas with cryogenic argon pellet injection. This technique is mostly limited in these experiments to the pre-TQ phase and quickly loses validity during the TQ. Two different cases are studied: a high (10 keV) temperature target and a low (4 keV) temperature target. The results indicate that early-time, low-energy (∼10 keV) hot electrons form ahead of the argon pellet as it enters the plasma, affecting the pellet ablation rate; it is hypothesized that this may be caused by rapid cross field transport of argon ions ahead of the pellet or by rapid cross field transport of hot electrons. Fokker–Planck modeling of the two shots suggests that the hot electron current is quite significant during the pre-TQ phase (up to 50% of the total current). Comparison between modeled pre-TQ hot electron current and post-TQ hot electron current inferred from avalanche theory suggests that hot electron current increases during the high-temperature target TQ but decreases during the low-temperature target TQ. The uncertainties in this estimate are large; however, if true, this suggests that TQ radial loss of hot electron current could be larger than previously estimated in DIII-D.

Pellet cloud characterisation, scaling and estimation of the material- and temperature distribution inside the cloud

Using spatially calibrated images of fast visible cameras, a database was established containing pellet cloud images and the related pellet- and plasma parameters. Using this database, two scalings were derived for the cloud size along the magnetic field lines as a function of pellet speed and ablation rate (first case) and pellet speed, pellet volume, plasma temperature and plasma density (second case). Using the images—based on the number of radiation maxima—the four main cloud shapes were also categorized. The isotope effect (the effect of hydrogen pellets in hydrogen or helium plasma) was also investigated with particular attention devoted to the cloud characteristics. Finally, a synthetic diagnostic—which simulates the measurement system and produces a synthetic pellet cloud image based on the output of the pellet cloud simulation—was developed to reveal the underlying density- and temperature distributions of the observed pellet cloud images. Using this synthetic diagnostic, one of the main identified cloud shapes was reconstructed. Our goal is to derive a scaling law for the toroidal extension of the pellet cloud at different pellet- and plasma conditions, to give a more reliable input for the pellet ELM triggering simulations and using these two results—a better understanding of the pellet-caused pressure perturbation.

Use of Ar pellet ablation rate to estimate initial runaway electron seed population in DIII-D rapid shutdown experiments

Small (2–3 mm, 0.9–2 Pa · m3) argon pellets are used in the DIII-D tokamak to cause rapid shutdown (disruption) of discharges. The Ar pellet ablation is typically found to be much larger than expected from the thermal plasma electron temperature alone; the additional ablation is interpreted as being due to non-thermal runaway electrons (REs) formed during the pellet-induced temperature collapse. Simple estimates of the RE seed current using the enhanced ablation rate give values of order 1–10 kA, roughly consistent with estimates based on avalanche theory. Analytic estimates of the RE seed current based on the Dreicer formula tend to significantly underestimate it, while estimates based on the hot tail model significantly overestimate it.

Simulation of pellet ablation for tokamak fueling with ITAPS front tracking

A magnetohydrodynamic numerical model and parallel software for the ablation of cryogenic deuterium pellets in the process of tokamak fueling has been developed based on the method of front tracking of ITAPS Center. The main features of the model are the explicit tracking of material interfaces, a surface ablation model, a kinetic model for the electron heat flux, a cloud charging and rotation model, and an equation of state accounting for atomic processes in the ablation cloud. The software was used for the first systematic studies of the pellet ablation rate and properties of the ablation channel in magnetic fields. Simulations revealed new features of the pellet ablation such as strong dependence of the radius of the ablation channel and ablation rate on the ‘warm-up’ time and supersonic spinning of the ablation channel.

Modelling of the pellet cloud evolution and mass deposition with an account of ∇B induced drift

Modelling of the pellet ablation cloud evolution including the ∇B induced drift motion is performed. The model includes cloud heating, expansion and ionization, acceleration in the low-field side (LFS) direction, Alfven conductivity of the background plasma, compensation of ∇B currents in different parts of the cloud during its propagation along the magnetic field, cooling of the background plasma and simulation of the pellet ablation rate in a self-consistent manner. The time evolution of cloud density and temperature profiles and the mass deposition after the pellet injection are calculated. The LFS and high-field side injection scenarios with plasma and pellet parameters typical for the ASDEX-Upgrade tokamak are compared. An effect of pre-cooling on the pellet penetration depth is studied. The calculated size of the neutral part of the cloud, the characteristic values of cloud density and temperature far from the pellet and the fuelling efficiency (for LFS pellets) are in reasonable agreement with those observed in experiments on the ASDEX-Upgrade.

Studies of the impurity pellet ablation in the high-temperature plasma of magnetic confinement devices

The ablation of impurity pellets in tokamak and stellarator plasmas is investigated. Different mechanisms for shielding the heat fluxes from the surrounding plasma to the pellet surface are discussed. A model for impurity pellet ablation is developed that can account for both neutral and electrostatic shielding. It is shown that the experimental values of the impurity pellet ablation rate are well described by the neutral gas shielding model over a wide range of plasma temperatures and densities. Taking into account the electrostatic shielding leads to worse agreement between the predictions of the model and the experimental data; this result still remains unclear. Scaling laws are obtained that allow one to estimate the local ablation rate of impurity pellets made of various materials over a wide range of plasma parameters in the neutral gas shielding model.

Modeling of the pellet cloud structure in the presence of ∇B induced drift

Modeling of the pellet ablation cloud evolution with account of the ∇B induced drift motion is performed. The model includes acceleration in the low-field-side direction, Alfven conductivity of the background plasma, compensation of ∇B currents in different parts of the cloud during its propagation along the magnetic field, cloud heating, expansion and ionization and simulation of the pellet ablation rate in a self-consistent manner. The time evolution of density and temperature profiles and the mass deposition after the pellet injection are calculated. The size of neutral part of the cloud, the characteristic values of cloud density and temperature far from the pellet and the fuelling efficiency are in a reasonable agreement with those observed in experiments on ASDEX-Upgrade tokamak.

3D adaptive mesh refinement simulations of pellet injection in tokamaks

We present results of Adaptive Mesh Refinement (AMR) simulations of the pellet injection process, a proven method of refueling tokamaks. AMR is a computationally efficient way to provide the resolution required to simulate realistic pellet sizes relative to device dimensions. The mathematical model comprises of single-fluid MHD equations with source terms in the continuity equation along with a pellet ablation rate model. The numerical method developed is an explicit unsplit upwinding treatment of the 8-wave formulation, coupled with a MAC projection method to enforce the solenoidal property of the magnetic field. The Chombo framework is used for AMR. The role of the E× B drift in mass redistribution during inside and outside pellet injections is emphasized.

Determination of q =1 surface by the variation of pellet ablation rate on the HL-1M

Strong drop of Hα emission has been observed on the HL-1M tokamak by means of a detector array while a pellet crosses the q=1 surface. In this article, the q=1 surface has been determined precisely by the interval and the shape of the Hα emission striations on the pellet trajectory due to the variation of pellet ablation rate. Theq-profile and current density distribution at the plasma centre region have been calculated according to the pellet ablation rate and the magnetic shear feature.

Measurement of cloud parameters near hydrogen and deuterium pellets injected into T-10 plasma

The clouds surrounding deuterium and hydrogen pellets with 0.3–1.4 mm sizes and 500–700 m s −1 velocities injected in the plasma core direction were studied experimentally. The cloud temperature profiles T c l( z) along the magnetic field direction were measured by means of the ratio of the line intensity I 1 to the continuum intensity I c for different minor radii. It was observed that T cl( z) profiles have a region with constant values of T cl ≈ 2–3 eV owing to the constant values of I 1, I c intensities. The toroidal size of this region varied with the pellet ablation rate. Far away from this region the cloud temperature increased with maximal absolute values of the space gradient dT cl dz = 0.30.6 eV cm −1 . The spatial gradient and the temperature in the centre of the profiles T cl(z) exhibit a weak dependence on the pellet ablation rate values.

Pellet fuelling deposition measurements on Jet and TFTR

The effective radial deposition profile of deuterium pellets injected into the Joint European Torus (JET) and the Tokamak Fusion Test Reactor (TFTR) has been determined from Thomson scattering diagnostic measurements of electron density taken immediately after pellet injection. The pellet ablation rate deduced from these measurements differs from that predicted by conventional pellet ablation theory. The possibility of enhanced radial transport during the ablation process has been examined to determine whether this can explain the difference between theory and experiment, but no evidence has been found to support such an explanation. The temporal evolution of the Balmer alpha light emitted during pellet ablation is found to be different from the effective pellet ablation rate determined from the density profile measurement. The authors conclude that the shielding mechanisms of conventional pellet ablation models have to be modified in order to predict and reproduce the observed effective ablation rate and penetration depth

The ablatant state of a hydrogen pellet during its passage in a tokamak

By considering the ablatant to be a 4-species (H2, H, H+ and e−) reacting gas and assuming the validity of local thermodynamic equilibrium, the ablatant state of a hydrogen pellet during its passage in a tokamak is studied. Results of analysis showed that the pellet ablation rate is sensitive neither to the specific assumption regarding the variation of the ratio of the specific heats, γ in the ablated cloud, nor to the precise ablation process at the pellet surface. Except a proportional constant depending on the effect of dissociation and ionization, the scaling of the pellet ablation rate with respect to the plasma state and pellet radius is similar to that of the 1-species neutral shielding model; the overall ablation rate is reduced by approximately 15%.The ratio ri/rp of the ionization radius, ri to the pellet radius, rp is shown to be related to the pressure, pe and the equilibrium constant of ionization, Ki(Te) by pe/Ki(Te) of the plasma electrons, and approaches a constant value, (≈ 11), when pe/Ki(te) > 2 × 10−12. For combinations of pellet radius, plasma state and magnetic field strength of interest, irrespective of the ionization process, at an ablated cloud radius r ≈ 2rp, nearly 80% of the ambient electron energy flux is absorbed.Under some situations when there is a lack of balance between the energy input of the plasma electrons and the heating and expansion of the ablatant, a weak shock (flow Mach number, M = 1) can develop near the pellet during the expansion of the ablatant.

Application of EMILAC to pellet injection.

A new type of elecromagnetic accelerator for pellet injection is proposed. Projectile of cylinder shape is accelerated with the repulsive force generated by a combination of two coils, which are different in purpose. And the accelerator is named EMILAC (Electro-Magnetic Inductive Linear Accelerator). In this papaer, we investigate the method of applying EMILAC to pellet injection, and calculate the ablation rate of pellet.

Vaporization mode and state of the ablatant of a deuterium pellet in tokamak discharges

The ablation of a deuterium pellet under prevailing tokamak discharge conditions is shown to be a dynamic phase transition process. An alternative boundary condition at the pellet surface is formulated. Computational results based on the new boundary condition showed that the state of the ablatant in the subsonic region depends on the boundary condition used but is hardly affected in the supersonic region. The scaling law of the pellet ablation rate, therefore, is insensitive to the boundary condition imposed.