Stephen F. Knowlton

V3FIT: a code for three-dimensional equilibrium reconstruction

The V3FIT code for performing equilibrium reconstruction in three-dimensional plasmas is described. It is a modular code that has the potential to be coupled with a variety of equilibrium solvers to compute the externally measured response to an arbitrary internal state of the plasma. Singular-value decomposition is used to identify the dominant components of the plasma state that can be accurately determined by the reconstruction process and to guide the minimization of the χ2 variance-normalized mismatch between the measured and computed signals. Comparison of a tokamak plasma equilibrium computed by V3FIT and by the axisymmetric equilibrium reconstruction code EFIT is presented. V3FIT is used to reconstruct an axisymmetric DIII-D equilibrium using experimentally observed magnetic diagnostic signals. Three-dimensional reconstructions of stellarator plasma equilibria in the CTH device show the code behaves as expected in the presence of experimental noise, appropriately ignores near-singular directions in parameter space and robustly reconstructs equilibria starting from substantially different initial parameter values.

Recent advances in the design of quasiaxisymmetric stellarator plasma configurations

Strategies for the improvement of quasiaxisymmetric stellarator configurations are explored. Calculations of equilibrium flux surfaces for candidate configurations are also presented. One optimization strategy is found to generate configurations with improved neoclassical confinement, simpler coils with lower current density, and improved flux surface quality relative to previous designs. The flux surface calculations find significant differences in the extent of islands and stochastic regions between candidate configurations. (These calculations do not incorporate the predicted beneficial effects of perturbed bootstrap currents.) A method is demonstrated for removing low order islands from candidate configurations by relatively small modifications of the configuration. One configuration is identified as having particularly desirable properties for a proposed experiment.

Power transmission and coupling for radiofrequency heating of plasmas

RF power is widely used as an auxiliary heating method in fusion devices. This paper reviews the relevant theoretical considerations for the ion cyclotron, lower hybrid and electron cyclotron ranges of frequency, and presents the history, the state of the art, and the plans and prospects for antennas and transmission lines for RF heating. Reactor-relevant concerns are discussed, and the information needed to develop realistic antenna designs for a reactor environment is assessed.

Design of the Compact Auburn Torsatron

This paper describes the design and optimization procedure for the Compact Auburn Torsatron. Included in this is a description of the Cary-Hanson Optimization technique. In this paper the properties of the magnetic fields are presented and a description of the machine and the construction procedure. The experimental setup for the surface mapping is described and conclusions are presented. 10 refs., 9 figs., 1 tab.

Non-axisymmetric equilibrium reconstruction for stellarators, reversed field pinches and tokamaks

Axisymmetric equilibrium reconstruction using magnetohydrodynamic equilibrium solutions to the Grad?Shafranov equation has long been an important tool for interpreting tokamak experiments. This paper describes recent results in non-axisymmetric (three-dimensional) equilibrium reconstruction of nominally axisymmetric plasmas (tokamaks and reversed field pinches (RFPs)), and fully non-axisymmetric plasmas (stellarators). Results from applying the V3FIT code to CTH and HSX stellarator plasmas, RFX-mod RFP plasmas and the DIII-D tokamak are presented.

Magnetic diagnostic responses for compact stellarators

The formulation of magnetic diagnostic response functions for a three-dimensional stellarator plasma is described. Reciprocity relations are used to compute unique response functions for each type of magnetic diagnostic. Green’s function response tables (databases) are generated from which both external coil and internal plasma current contributions to diagnostic signals can be rapidly computed. Applications to compact stellarators are described.

Control of magnetic islands with horizontal field trim coils in a low aspect ratio torsatron

The presence of large magnetic islands associated with rational magnetic surfaces in toroidal fusion devices can lead to a reduction of the confinement time of plasmas in such devices. In stellarators and torsatrons, the island size is usually minimized by careful design and coil construction within close tolerances in order to reduce the effect of error fields. In addition, magnetic islands resulting from unavoidable error fields can be reduced or eliminated through the use of auxiliary trim coils. The Compact Auburn Torsatron has been equipped with two pairs of large Helmholtz coils producting mutually orthogonal magnetic fields in the horizontal plane. These trim coils are used to control the size and phase of the t=1/2 magnetic island. A reduction of the inherent t=1/2 magnetic island size by a factor of three is achieved through a systematic variation of both horizontal trim field components. The minimization of the island size occurs simultaneously with the largest poloidal rotation rate of the island as a function of the correction coil current

Experimental studies of the radial diffusion of energetic electrons in lower‐hybrid wave heated plasmas in the Alcator‐C tokamak

An upper limit for the cross‐field spatial diffusion coefficient of energetic electrons in moderate density tokamak discharges has been measured. The energetic electrons were generated by square wave‐modulated lower‐hybrid (LH) wave injection. The decay of the fast electron population for electron energies ed≥100 keV following LH radio‐frequency (RF) power shutoff was inferred from the time dependence of the radial profiles of the hard x‐ray bremsstrahlung emission. The experimental results were fitted to a diffusive model that includes collisional losses and electric field acceleration. The fast electron diffusion coefficient consistent with the data is Df≤0.2 m2/s, at least in the inner half of the plasma. The corresponding global confinement time of the energetic electrons is estimated to be at least a factor of 2 greater than the energy confinement time of the bulk plasma in discharges of density ne=8×1019 m −3.

Magnetic configuration studies in a compact Torsatron

An overview is presented of an experimental program of magnetic field line mapping on the research-grade Compact Auburn Torsatron (CAT). The vacuum magnetic flux surfaces of the CAT device have been experimentally mapped in a variety of magnetic configurations. The results are compared with an extensive computer model in order to validate the coil design. In initial field mapping experiments, an up-down asymmetry was identified in the vacuum magnetic surfaces, and was corrected with the use of a radial trim field. Magnetic islands are observed and their size has been reduced, also through the use of auxiliary trim coils. The Compact Auburn Torsatron is equipped with two pairs of large Helmholtz coils producing mutually orthogonal magnetic fields in the horizontal plane, and two pairs of helical saddle coils wound directly on the toroidal vacuum vessel. These trim coils are used to control the size and phase of the t=1/2 magnetic island. Through a systematic variation of trim field components, we demonstrate a reduction of the inherent t=1/2 magnetic island size by a factor of three. The technique is applicable to correcting small error fields in larger helical confinement devices. The measurements of island size are compared with measurements of magnetic field line rotation within the island, and are found to be in good agreement with first-order perturbation theory.

Design and implementation of a multichannel millimeter wave interferometer for the Compact Toroidal Hybrid experiment.

A three-channel 1 mm wave interferometer has been designed, assembled, and installed on the Compact Toroidal Hybrid torsatron (CTH). The interferometer design makes novel use of a subharmonic mixer for detection, which simplifies alignment. It employs a single electronically tunable source that is repetitively chirped using a sawtooth waveform of frequency up to 1 MHz. The 15.25 GHz drive oscillator is multiplied in two stages to 122 GHz before a final doubler stage brings it to 244 GHz. Local oscillator (LO) power at 122 GHz is directed through waveguide to the LO input of the subharmonic mixer of each viewing chord, simplifying alignment. Phase detection is performed by directly digitizing the amplified mixer outputs at 50 MHz and processing them with a software algorithm. Initial measurements made with the central chord of the new interferometer agree with those from the existing 4 mm system at low densities. The 1 mm system performs well in current-driven discharges reaching densities over 10(19) m(-3), whereas the lower frequency interferometer is found to be less reliable due to loss of fringes. This is a critical improvement for experiments studying the onset, avoidance, and vacuum magnetic transform dependence of disruptions in the CTH device.