Thomas D. Rognlien

On the exploration of innovative concepts for fusion chamber technology

Abstract This study, called APEX, is exploring novel concepts for fusion chamber technology that can substantially improve the attractiveness of fusion energy systems. The emphasis of the study is on fundamental understanding and advancing the underlying engineering sciences, integration of the physics and engineering requirements, and enhancing innovation for the chamber technology components surrounding the plasma. The chamber technology goals in APEX include: (1) high power density capability with neutron wall load >10 MW/m 2 and surface heat flux >2 MW/m 2 , (2) high power conversion efficiency (>40%), (3) high availability, and (4) simple technological and material constraints. Two classes of innovative concepts have emerged that offer great promise and deserve further research and development. The first class seeks to eliminate the solid “bare” first wall by flowing liquids facing the plasma. This liquid wall idea evolved during the APEX study into a number of concepts based on: (a) using liquid metals (Li or Sn–Li) or a molten salt (Flibe) as the working liquid, (b) utilizing electromagnetic, inertial and/or other types of forces to restrain the liquid against a backing wall and control the hydrodynamic flow configurations, and (c) employing a thin (∼2 cm) or thick (∼40 cm) liquid layer to remove the surface heat flux and attenuate the neutrons. These liquid wall concepts have some common features but also have widely different issues and merits. Some of the attractive features of liquid walls include the potential for: (1) high power density capability; (2) higher plasma β and stable physics regimes if liquid metals are used; (3) increased disruption survivability; (4) reduced volume of radioactive waste; (5) reduced radiation damage in structural materials; and (6) higher availability. Analyses show that not all of these potential advantages may be realized simultaneously in a single concept. However, the realization of only a subset of these advantages will result in remarkable progress toward attractive fusion energy systems. Of the many scientific and engineering issues for liquid walls, the most important are: (1) plasma–liquid interactions including both plasma–liquid surface and liquid wall–bulk plasma interactions; (2) hydrodynamic flow configuration control in complex geometries including penetrations; and (3) heat transfer at free surface and temperature control. The second class of concepts focuses on ideas for extending the capabilities, particularly the power density and operating temperature limits, of solid first walls. The most promising idea, called EVOLVE, is based on the use of a high-temperature refractory alloy (e.g. W–5% Re) with an innovative cooling scheme based on the use of the heat of vaporization of lithium. Calculations show that an evaporative system with Li at ∼1 200°C can remove the goal heat loads and result in a high power conversion efficiency. The vapor operating pressure is low, resulting in a very low operating stress in the structure. In addition, the lithium flow rate is about a factor of ten lower than that required for traditional self-cooled first wall/blanket concepts. Therefore, insulator coatings are not required. Key issues for EVOLVE include: (1) two-phase heat transfer and transport including MHD effects; (2) feasibility of fabricating entire blanket segments of W alloys; and (3) the effect of neutron irradiation on W.

Verification of frequency scaling laws for capacitive radio‐frequency discharges using two‐dimensional simulations*

Weakly ionized processing plasmas are studied in two dimensions using a bounded particle‐in‐cell (PIC) simulation code with a Monte Carlo collision (MCC) package. The MCC package models the collisions between charged and neutral particles, which are needed to obtain a self‐sustained plasma and the proper electron and ion energy loss mechanisms. A two‐dimensional capacitive radio‐frequency (rf) discharge is investigated in detail. Simple frequency scaling laws for predicting the behavior of some plasma parameters are derived and then compared with simulation results, finding good agreements. It is found that as the drive frequency increases, the sheath width decreases, and the bulk plasma becomes more uniform, leading to a reduction of the ion angular spread at the target and an improvement of ion dose uniformity at the driven electrode.

Analytic model of power deposition in inductively coupled plasma sources

A simple analytic model valid for all collisionality regimes is developed to describe the power deposition in a cylindrical inductively coupled plasma source with a planar coil. The heating is ohmic at high pressures and remains finite at low pressures. The low‐pressure collisionless heating is due to kinetic nonlocal effects. The model is in good agreement with other calculations of collisionless heating. A diffusion model is then used to determine the plasma density profile and the electron temperature in terms of the gas pressure and the source geometry. The heating and diffusion models are used to determine the scaling of the inductive electric field with applied frequency and input power, and the results are compared with published experimental data to verify the scaling.

Modeling Electronegative Plasma Discharges

A macroscopic analytic model for a three-component electronegative plasma has been developed. Assuming the negative ions to be in Boltzmann equilibrium, a positive ion ambipolar diffusion equation is found. The electron density is nearly uniform, allowing a parabolic approximation to the plasma profile to be employed. The resulting equilibrium equations are solved analytically and matched to an electropositive edge plasma. The solutions are compared to a simulation of a parallel-plane r.f. driven oxygen plasma for two cases: (1) p=50 mTorr, neo = 2.4x10 (15) m-3, and (2) 10 mTorr, new = 1.0x10 (16) m-3. In the simulation, for the low power case (1), the ratio of negative ion to electron density was found to be alpha sub 0 is almost equal to 8, while in the higher power case alpha sub 0 is almost equal to 1.3. Using an electorn energy distribution that approximates the simulation distribution by a two-temperature Maxwellian, the analytic values of alpha sub zero are found to be close to, but somewhat larger, than the simulation values. The average electron temperature found self-consistently in the model is close to that in the simulation. The results indicate the need for determining a two-temperature electron distribution self-consistently within the model.

ALPS–advanced limiter-divertor plasma-facing systems

The advanced limiter-divertor plasma-facing systems (ALPS) program was initiated in order to evaluate the potential for improved performance and lifetime for plasma-facing systems. The main goal of the program is to demonstrate the advantages of advanced limiter:divertor systems over conventional systems in terms of power density capability, component lifetime, and power conversion efficiency, while providing for safe operation and minimizing impurity concerns for the plasma. Most of the work to date has been applied to free surface liquids. A multi-disciplinary team from several institutions has been organized to address the key issues associated with these systems. The main performance goals for advanced limiters and divertors are a peak heat flux of \ 50 MW:m 2 , elimination of a lifetime limit for erosion, and the ability to extract useful heat at high power conversion efficiency (40%). The evaluation of various options is being conducted through a combination of laboratory experiments, www.elsevier.com:locate:fusengdes

Thermal heat flux in a plasma for arbitrary collisionality

The thermal heat flux along a uniform magnetic field due to a temperature gradient is calculated using a Monte Carlo solution to the Fokker–Planck equation. This numerical solution, which is computed for a particular electron temperature profile, is valid for arbitrary mean‐free‐path, λmfp. The calculated heat flux makes a smooth transition between the analytic expressions for the short and long λmfp limits.

Transitions of turbulence in plasma density limits

A series of BOUT [X. Q. Xu et al., Phys. Plasmas 7, 1951 (2000)] simulations is conducted to investigate the physical processes which limit the density in tokamak plasmas. Simulations of turbulence in tokamak boundary plasmas are presented which show that turbulent fluctuation levels and transport increase with collisionality. At high edge density, the perpendicular turbulent transport dominates the parallel classical transport, leading to substantially reduced contact with divertor plates and the destruction of the edge shear layer, and the region of high transport then extends inside the last closed flux surface. As the density increases these simulations show resistive X-point mode→resistive ballooning modes. The simulations also show that it is easier to reach the density limit as the density increases while holding pressure constant than holding temperature constant. A set of 2D transport simulations with increasingly large radial outboard transport, as indicated by BOUT for increasing density, shows...

Initial physics results from the National Spherical Torus Experiment

The mission of the National Spherical Torus Experiment (NSTX) is to extend the understanding of toroidal physics to low aspect ratio (R/a approximately equal to 1.25) in low collisionality regimes. NSTX is designed to operate with up to 6 MW of High Harmonic Fast Wave (HHFW) heating and current drive, 5 MW of Neutral Beam Injection (NBI) and Co-Axial Helicity Injection (CHI) for non-inductive startup. Initial experiments focused on establishing conditions that will allow NSTX to achieve its aims of simultaneous high-bt and high-bootstrap current fraction, and to develop methods for non-inductive operation, which will be necessary for Spherical Torus power plants. Ohmic discharges with plasma currents up to 1 MA and with a range of shapes and configurations were produced. Density limits in deuterium and helium reached 80% and 120% of the Greenwald limit respectively. Significant electron heating was observed with up to 2.3 MW of HHFW. Up to 270 kA of toroidal current for up to 200 msec was produced noninductively using CHI. Initial NBI experiments were carried out with up to two beam sources (3.2 MW). Plasmas with stored energies of up to 140 kJ and bt =21% were produced.

Edge-plasma models and characteristics for magnetic fusion energy devices

A description is given of the models and resulting characteristics of the plasma adjacent to material surfaces that comprise the divertor and first wall of magnetic fusion energy devices under normal operation conditions. This thin edge-plasma region begins a short distance inside of the so-called separatrix, which divides the core domain of confined magnetic field lines from the scrape-off layer domain of open fields lines that pass through material surfaces; edge transport simulations give a unified description of the plasma throughout this region. In addition to the plasma fuel components escaping from the core (i.e. deuterium and tritium ions and their neutralizing electrons), models are included for neutral gas and impurities evolved from surfaces or injected. The confining magnetic field, B, is generally large enough to provide substantial enhancement of confinement normal to B compared to along B, resulting in steep cross-field gradients of plasma parameters. Three distinct types of edge-plasmas are illustrated, depending on the plasma collisionality, which are named as follows: sheath-limited, high-recycling, and detached plasmas. Examples of each type are given, together with the corresponding plasma conditions produced at the material surface boundaries. Detailed results are presented for the edge-plasmas of the ARIES-AT and FIRE tokamak designs. The edge-plasma characteristics calculated here provide the plasma profiles needed for other codes which perform detailed modeling of plasma sheath formation, surface modification via sputtering/redeposition, and recycled neutral-particle transport as detailed by other papers in this issue.

Induced magnetic-field effects in inductively coupled plasmas

In inductive plasma sources, the rapid spatial decay of the electric field arising from the skin effect produces a large radio frequency (RF) magnetic field via Faraday’s law. It was previously shown that this magnetic field leads to a reduction of the electron density in the skin region, as well as a reduction in the collisionless heating rate. The electron deficit leads to the formation of an electrostatic potential which pulls electrons in to restore quasineutrality. Here the electron density calculation is extended to include both the induced and electrostatic fields. If the wave frequency is not too low, the ions respond only to the averaged fields, and hence the electrostatic field is oscillatory, predominantly at the second harmonic of the applied field. The potential required to establish a constant electron density is calculated and compared with numerical orbit‐code calculations. For times short compared to ion transit times, the quasineutral density is just the initial ion density. For timescal...