An analysis and successful benchmarking of the Chapman-Enskog-like (CEL) continuum kinetic closure approach algorithm in NIMROD
Not Available
Jepson, Joseph R. (ORCID:0000000299924056)↗
Engineering topics
Held, Eric D.
Publications and source records attributed to Held, Eric D..
Final Report for Center for Tokamak Transient Simulations at USU
Providing plasma fluid codes like NIMROD with continuum drift kinetic (CDK) physics that is quantitatively valid and computationally feasible throughout the spatial domain is difficult. Work at Utah State University (USU), in collaboration with the Center for Tokamak Transient Simulations (CTTS), focused on applying CDK closures in disruption-related calculations. Three examples where kinetic physics is paramount are (1) the electron stress tensor closure in Ohms law for accurately describing neoclassical tearing mode (NTM) evolution, (2) runaway electron (RE) density (nRE) and current (jRE) moments in NIMROD’s extended MHD model for self-consistent evolution of RE populations during disruptions and, (3) energetic ion effects on a myriad of MHD instabilities. While NTM simulations and continuum and PIC approaches to energetic ions in NIMROD have been a major goals of USU’s closure work for several years, the development of self-consistent CDK RE capability in NIMROD was started and extended considerably during the CTTS effort. Some goals of CDK RE in NIMROD are to explore the effects of the 2D relativistic phase space in 4D simulations and compare with NIMROD’s fluid RE model. Four publications and two PhD theses came out of the USU CTTS effort.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Moment-Fourier approach to ion parallel fluid closures and transport for a toroidally confined plasma
A general method of solving the drift kinetic equation is developed for an axisymmetric magnetic field. Expanding a distribution function in general moments, a set of ordinary differential equations is obtained. Successively expanding the moments and magnetic-field involved quantities in Fourier series, a set of linear algebraic equations is obtained. The set of full (Maxwellian and non-Maxwellian) moment equations is solved to express the first-order density, temperature, and flow velocity in terms of radial gradients of the zeroth-order pressure and temperature. Closure relations that connect parallel heat flux density and viscosity to the radial gradients and parallel gradients of temperature and flow velocity are also obtained by solving the non-Maxwellian moment equations. The closure relations combined with the linearized fluid equations reproduce the same solution obtained directly from the full moment equations. Furthermore, the method can be generalized to derive closures and transport for an electron-ion plasma and a multi-ion plasma in a general magnetic field.
neoclassical transport↗
Accurate numerical, integral methods for computing drift-kinetic Trubnikov-Rosenbluth potentials
A novel numerical method is employed to compute the integral form of the axi-symmetric Trubnikov-Rosenbluth potentials. Two methods for quadrature in pitch-angle are described and their convergence properties are studied. Careful attention is given to quadrature over a singular Green's function. Here it is shown that an infinite series representation of the Green's function can be used more efficiently than its closed form involving complete elliptic integrals. Then a collocation method in speed, with its associated quadrature scheme, is laid out and its convergence properties are studied. Using the proposed scheme, accurate low-order moments of the field collision operator are obtained using relatively few velocity space degrees of freedom. The scheme is showcased by solving for the equilibrium, axi-symmetric bootstrap current in tokamaks. A C 0 Gauss-Lobatto-Legendre finite element pitch-angle basis with vertex nodes at the trapped/passing boundary is shown, in the context of the integral methods used, to be much more efficient than the more common Legendre polynomial expansion.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Moments of the Boltzmann collision operator for Coulomb interactions
Exact moments of the Boltzmann collision operator are calculated in the irreducible Hermitian moment expansion written in terms of the random-velocity variable of each species. The formulas are presented in closed, algebraic form and can be straightforwardly implemented in computer algebra systems. They are valid for two arbitrary masses, temperatures, and flow velocities, and hence include all other existing results derived for distribution functions expanded with respect to reference states of one temperature and flow velocity. In comparison, the Landau collisional moments are good approximations for large Coulomb logarithm and small relative flow velocity, but they fail to predict the correct behavior of most collisional moments for large relative flow even for weakly coupled plasmas.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Potential, field, and interactions of multipole spheres: Coated spherical magnets
Not Available
Ji, Jeong-Young↗
Transport coefficients for magnetic-field evolution in inviscid magnetohydrodynamics
The magnetized resistivity and electrothermal tensors when substituted into the induction equation lead to electrothermal magnetic field generation, resistive magnetic diffusion, and magnetic field advection due to resistivity gradients, temperature gradients and currents. Here, the advection terms driven by temperature gradient and current have cross-field components (perpendicular to both the magnetic field and the driving term) that depend on significantly modified versions of Braginskii’s transport coefficients. The improved fits to Braginskii’s coefficients given by Epperlein and Haines and Ji and Held give physically incorrect results for cross-field advection at small Hall parameters (product of cyclotron frequency and collision time). The errors in Epperlein and Haines’ fits are particularly severe, giving increasing advection velocities below a Hall parameter of one when they should decrease linearly to zero. Epperlein and Haines’ fits can also give erroneous advection terms due to variations in effective atomic number. The only serious error in Braginskii’s fits is an overestimate in advection due to perpendicular resistivity. New fits for the cross-field advection terms are obtained from a direct numerical solution of the Fokker-Planck equation and Ji and Held’s higher order expansion approach that are continuous functions of the effective atomic number.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Maxwell–Boltzmann statistics of the quantum ideal gas in the canonical ensemble
Abstract The Maxwell–Boltzmann statistics of the quantum ideal gas is studied through the canonical partition function by exactly counting discrete quantum states without the continuum approximation. Analytic expressions for energy, pressure, entropy, and heat capacity are expressed in terms of Jacobi theta functions and complete elliptic integrals. The results show typical effects of discrete energy levels in the low temperature limit while they reproduce thermodynamics of the classical ideal gas in the high temperature limit.
Mechanics↗