MHD Stability and Turbulence

Animations of MHD Turbulence



High temperature magnetically confined plasmas can exhibit a rich variety of MHD (magneto-hydrodynamic) behavior. This generally is observed as some form of nonlinearly saturated turbulence which has been preceded by a linear growth phase. The goals of computational MHD theory are to first understand the causes and dynamics of this turbulence and then to seek ways to minimize or avoid it through control of plasma parameters, plasma shape or machine design.

The following results will be specific to shear Alfvén waves de-stabilized by energetic particles. These instabilities are of current interest due to their relevance to ignited, power-producing fusion devices. Such systems run with a mixture of deuterium (D) and tritium (T) fuel. One of the by-products of the DT reaction is a high energy (3.5 Mev) alpha (Helium-4) particle. The energetic alpha population can destabilize a variety of shear Alfvén waves, leading to new forms of turbulence which are not present in current non-ignited experiments.

Scientific visualization of MHD phenomena

Scientific visualization has proven a useful tool for analyzing MHD instabilities. Due to the fact that plasmas are best confined in toroidal (doughnut-shaped) magnetic geometries, the instability mode structure is necessarily 3-D and can become complicated due to the twisted nature of the magnetic field lines. Scientific visualization has been useful in the following aspects: (1) identification of new phenomena one otherwise might not look for, (2) developing a better intuitive understanding of the problem, (3) checking for errors in the simulation, (4) more effectively communicating the results. All figures shown here have been rendered directly from the output of the TAE/FL 3-D initial value code. This is based on a gyrofluid model with Landau closure which has been described in: Physics of Fluids vol. B 4, pg. 3316, Oct., 1992, also, see Physics of Plasmas vol. 1, pg. 1503, May, 1994. The scientific visualization software used here is AVS (AVS is a trademark of Advanced Visual Systems, Inc., Waltham, MA).

Magnetic field geometry/TAE mode structure

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Here we have displayed a magnetic flux isosurface with a few circuits of a magnetic field line (shown in white). The field lines wrap around the torus, circulating in both the long way around (toroidal direction) and the short way around (poloidal direction). On rational surfaces, the ratio of the poloidal and toroidal winding rates forms a rational number and the field lines close on themselves. On the nearby irrational surfaces the field lines are unclosed. This isosurface is colored using the potential variation of a toroidal Alfvén (TAE) instability, showing that the pitch of its mode structure nearly matches that of the equilibrium confining magnetic field. This alignment with the magnetic field is characteristic of a number of plasma instabilities and is often useful as an approximation to simplify analytic descriptions.


Nonlinear Evolution of Alfvén (TAE) Turbulence

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The above figure illustrates the changes in the 3 dimensional mode structure which occur for a tokamak TAE instability as it evolves from the initial linearly unstable state (top figure) to a saturated nonlinear state (bottom figure). This instability starts out with a well-defined helical structure which approximately follows the local magnetic field line geometry. In the saturated state, much of the original structure has been destroyed. As the turbulence evolves, strong velocity shearing occurs which breaks up much of the original helical filamentary structure.


Ray traced internal structure/nonlinear self-organization

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The above figure demonstrates the use of ray-tracing to visualize the internal mode structure of a TAE instability. This allows the physicist to effectively take an x-ray of the volume and see both internal and external features of the mode structure by appropriately adjusting the transparency of the data. This figure shows the electrostatic potential variations of a TAE instability in its linear growth phase. A filamentary mode structure is apparent with gradients much weaker along the magnetic field direction than perpendicular to it. This is a common property of MHD instabilities and is related to the presence of a strong confining toroidal magnetic field. To look at the same simulation later in time in the nonlinear saturated phase, click here for SMALL VERSION or here for LARGER VERSION. This image shows the effects of nonlinear self-organization (i.e., the structure has become simpler) which can be an important aspect of the nonlinear saturation of such instabilities.


Volume-Rendered internal structure

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In addition to ray-tracing, an alternative way to view internal MHD structures is through volume-rendering. Ray-tracing images show volume-integrated information (i.e., the color of each pixel is influenced by an accumulation of color and transparency information from the volume elements or voxels which the associated ray has passed through). Volume rendering is based on a more direct mapping of the color and transparency of each 3-D voxel onto a 2-D image plane. The above image shows the the mode structure in the linear regime. Click here for SMALL VERSION or here for LARGER VERSION to see the same simulation later in time during the nonlinear saturated phase.


Two-dimensional color contour slices/ ballooning modes

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Some instabilities develop relatively small scale variations which can be more accurately visualized by taking a two-dimensional perpendicular slice through a section of the torus. In the above figure such a slice is shown for a "ballooning instability." This name refers to the fact that this instability bulges out more on the outside half of the torus (where the drive is stronger) than on the inside half. As can be seen from the figure, the mode structure is more coherent and larger scale on the outside (right- hand side) than on the inside (left-hand side).


Extruded 2-D slices

A useful technique for enhancing detailed structure in 2-D perpendicular slices (as shown above) is to extrude or add elevation based on the value of the data. The following examples illustrate this method.


(a) Nonlinear saturation mechanisms

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The above pair of figures demonstrate the nonlinear generation of sheared velocity flows for a saturated TAE instability. The right-hand figure shows the total electrostatic potential, including nonlinearly generated terms. A deep vortex structure is generated which implies sheared velocity flows (proportional to the gradient of potential). The left-hand figure indicates the potential without the dominant nonlinear Fourier component. This allows one to see how the initially coherent linear mode structure becomes fragmented and suppressed by the sheared flow velocities.


(b) Experiment-theory comparison

Visualization can also be a useful tool for direct experiment/theory comparisons. Click here for SMALL VERSION or here for LARGER VERSION to see an example of such a comparison. The left hand picture is based upon chordal x-ray emissivity experimental data (this is a function of the fluctuating plasma temperature and density) taken from the W7-AS stellarator experiment. The right-hand figure shows results of a theoretical simulation, allowing the physicist to quickly identify both areas of similarity and dissimilarity. For further details of this particular example, see Physical Review Letters, vol. 72, no. 8, pg. 1220, Feb. 21, 1994.