The effect of aspect ratio on magnetic field fluctuations in reversed-field pinches is investigated using a three-dimensional magnetohydrodynamic code. Configurations with aspect ratios of 1.1, 2.2, and 4.4 are modeled. The results are extrapolated to aspect ratio 8.8 for comparison with the Extrap T1 experiment [Nucl. Fusion 34, 427 (1994)]. It is found that the average modal amplitudes decrease with aspect ratio. However, the spectrum broadens correspondingly, resulting in negligible effect on the magnetic fluctuation level. The computed spectrum dynamics are found to be in good agreement with experimental observations on the T1 experiment. Quantitative evaluations of the field line stochasticity indicate no dependence of the mean magnetic field diffusion rate on aspect ratio.

Scaling laws for reversed field pinch (RFP) confinement parameters versus plasma current and density are found from computer simulations. The RFP dynamics at high Lundquist numbers approaching 106 is studied using a high resolution, 3-D, resistive MHD numerical code. Optimum plasma conditions are attained by assuming that the transport coefficients are classical, and by ignoring radiation losses and resistive wall effects. Anomalous global transport results from classical parallel heat conduction along stochastic field lines in the plasma core. The pinch parameter is Θ = 1.8 and the aspect ratio is R/a = 1.25. Poloidal beta is found to scale as βθ ∝ (I/N)-0.40I-0.40 and energy confinement time as τE ∝ (I/N)0.34I0.34. On-axis temperature scales as T(0) ∝ (I/N)0.56I0.56. Experimental results from T2, RFX and MST agree well with the above numerical results and also with the obtained magnetic fluctuation scaling ∝ S-0.14, where S is the Lundquist number. Thus stochastic core field lines appear to persist also at higher, reactor relevant currents and temperatures in the conventional RFP, indicating the need to further pursue confinement enhancement techniques.

A time-spectral method for solution of initial value partial differential equations is outlined. Multivariate Chebyshev series are used to represent all temporal, spatial and physical parameter domains in this generalized weighted residual method (GWRM). The approximate solutions obtained are thus analytical, finite order multivariate polynomials. The method avoids time step limitations. To determine the spectral coefficients, a system of algebraic equations is solved iteratively. A root solver, with excellent global convergence properties, has been developed. Accuracy and efficiency are controlled by the number of included Chebyshev modes and by use of temporal and spatial subdomains. As examples of advanced application, stability problems within ideal and resistive magnetohydrodynamics (MHD) are solved. To introduce the method, solutions to a stiff ordinary differential equation are demonstrated and discussed. Subsequently, the GWRM is applied to the Burger and forced wave equations. Comparisons with the explicit Lax-Wendroff and implicit Crank-Nicolson finite difference methods show that the method is accurate and efficient. Thus the method shows potential for advanced initial value problems in fluid mechanics and MHD.

No abstract

A series of high resolution, 3D, resistive MHD numerical simulations of the reversed-field pinch are performed to obtain scaling laws for poloidal beta and energy confinement at Lundquist numbers approaching 10(6). Optimum plasma conditions are attained by taking the transport coefficients to be classical, and ignoring radiation losses and resistive wall effects. We find that poloidal beta scales as beta(straight theta) approximately I-0.40 and that the energy confinement time scales as tau(E) approximately I0.34 for fixed I/N, with aspect ratio R/a = 1.25.