G.A. Emmert

Simulation of poloidal divertors in one-dimensional tokamak transport codes

The two-dimensional effect of plasma flow along the field lines in the scrape-off zone of a poloidal divertor has been modelled phenomenologically in a one-dimensional tokamak transport code. Some results for the density and temperature profiles in the scrape-off zone, as well as in the main plasma, are given in this paper. These calculations suggest some approximations, which have been used to develop a zero dimensional model of the divertor; this model can be used to make estimates of divertor performance without having to make detailed numerical calculations.

A kinetic model for divertors and pumped limiters

In divertors and pumped limiters, plasma flows along magnetic field lines from the scrape-off layer to a material wall where it is neutralized. The neutrals refluxing from the wall will undergo ionization and charge exchange, producing cold ions. This problem has been examined by using a largely analytical, collisionless kinetic model which includes the effects of charge exchange. Cases with uniform magnetic field and with magnetic fields possessing a constriction (as in a bundle divertor) are treated. The cold ions increase the electric potential over that which otherwise would exist. Solutions are found with a peak in the potential near the plate, with cold ions flowing down the potential gradient either toward the scrape-off zone or towards the wall, depending on where they are produced. This is in agreement with the predictions of fluid theories and numerical kinetic calculations. The net effect is to reduce the heat flux in hot ions to the divertor plate, desirable for reducing sputtering loss. This analytical approach can be used to produce computationally efficient routines to determine particle and energy losses from the scrape-off layer which are suitable for inclusion in transport codes.

Non-ambipolar transport in a magnetic divertor

Plasma transport is studied in a simulated magnetic divertor in the Wisconsin single-ring DC machine. The transport perpendicular and parallel to the magnetic field is shown to be non-ambipolar by a variety of measurements. The degree of the non-ambipolarity can be reduced by an appropriately designed divertor target plate, but not eliminated altogether. The density and temperature profiles in the scrape-off zone agree with the solutions of one-dimensional transport equations that assume classical cross-field diffusion due to ion-neutral collisions, classical cross-field conductivity due to electron-neutral collisions, and plasma flow parallel to the field at the local ion acoustic velocity.

Transfer function analysis of a stable and feedback-stabilized plasma

The transfer function of a magnetic mirror plasma containing a feedback loop is measured experimentally. The measurements are obtained in a configuration where 1) the interchange mode is weakly damped, and 2) the interchange mode is unstable, but stabilized by the feedback loop. The results are in good agreement with the theoretically derived transfer function involving parameters (e.g. damping rates) determined by fitting the theoretical curve to the data. This method of analysis has diagnostic utility for mode identification and the measurement of damping rates.

Experimental transfer function analysis of a dissipative and a reactive mode

Experimental measurements of the transfer function of both a dissipative and a reactive instability in the same device — the Linear Multi-Mirror experiment — are reported. The results illustrate clearly the dissipative and reactive nature of each mode and are consistent with the theoretical form of the transfer function.

A variational calculation of the trapping rate in thermal barriers

A variational calculation of the trapping rate and trapped-ion density in thermal barriers is presented. The effects of diffusion in energy as well as pitch-angle scattering are retained. The variational formulation uses the actual trapped/passing boundary in velocity space. The boundary condition is that the trapped-ion distribution function match the passing-ion distribution function, which is taken to be a Maxwellian, on the boundary. The results compare well with the two-dimensional Fokker-Planck code calculations by Futch and LoDestro. The CPU time for a variational calculation is less than 0.1 s using the CRAY-I computer, while a typical Fokker-Planck code calculation takes 10–20 min.

Time evolution of ECRH power deposition in a tandem mirror plasma

A mechanism has been developed by which a three-dimensional Electron Cyclotron Resonance Heating (ECRH) ray-tracing-absorption calculation may be coupled to a tandem mirror transport code. The radial temperature and density profiles of the transport code are expanded via flux conservation to provide the three-dimensional geometry required for the ray-tracing calculation. Absorption along the ray trajectory determines an equivalent radial ECRH power deposition profile for use by the transport code. This profile must be generated by using multiple ray-tracing calculations to simulate the spatial spread of the power launched from an antenna. A technique for artificially producing these multiple ray simulations is presented and compared with results where multiple ray-tracing calculations were performed. Examples of plasma build-up simulations for a tandem mirror using ECRH in the plug are provided. A positive feedback mechanism is identified which produces locally large electron temperatures. This occurs frequently near the plasma edge, shielding the electrons near the plasma axis from the incident ECRH power, and producing a hollow temperature profile. This may lead t o the collapse of the plug plasma.

Light-atom neutral beams for tandem mirror end plugs

The advantages and feasibility of neutral beams with Z ? 3 formed from negative ions, accelerated to 0.5?1.0 MeV?amu?1, and neutralized, are investigated for use in tandem mirror reactor end plugs. A reactor plasma physics design incorporating these beams has been done with the result that such a reactor could produce Qs (ratio of fusion power to injected power) of 20?30. These beams thus might be a replacement for the currently proposed 200?500-keV neutral proton beams presently planned for tandem mirror reactors. Thus these Z ? 3 neutral beams could increase the potential attractiveness of tandem mirror reactors by offering a possible substitute for difficult high-energy neutral-hydrogen end plug beams.

Time-dependent studies of a tandem mirror with thermal barriers

The time evolution of a plasma confined in a tandem mirror with thermal barriers has been studied. A physics model is given which describes the kinetic interactions in velocity space between the particles of the various plasma species that exist in each spatial region of the confinement, and the effects of a variety of particle and energy sources applied to the plasma. The analysis includes particle and energy rate equations for the various species determining the plasma confinement. The analysis also includes quasi-neutrality and ambipolarity conditions which define the ambipolar potential profile along the axis of the device as well as expressions for the passing particle densities in each region. This model describes in a self-consistent manner the time evolution of tandem mirror confinement with thermal barriers including the steady-state phase of operation. The resulting system of equations is solved numerically. The axicell MFTF-B configuration has been studied specifically. A possible startup scenario has been obtained. The results show the time sequence that must be followed to build up a plasma from given initial conditions to the steady-state phase by means of appropriately programmed particle and energy sources applied to the plasma.

Properties and solutions of the steady-state neoclassical transport equations

Some results on the properties and solutions of the steady-state form of the neoclassical transport equations are presented for regimes of interest to feasibility experiments and reactors. An analytical solution is obtained for the special case dT/dr = 0. For dT/dr ≠0, an analytic solution is found for the particle density n(r) in terms of the current j(r) and the temperature T(r). For a prescribed j(r), a single differential equation remains to find the temperature profile. The numerical results suggest that neoclassical scaling does not admit self-sustained fusion plasma operation (n ~ 1014/cm3, T ~ 10 keV) except in plasmas of uninterestingly small sizes (Ip <500 kA).