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Hirshman, S.P.

Oak Ridge National Lab., TN (USA)

Oak Ridge National Lab., TN (USA)

AbstractAbstract

[en] By rearranging terms in a polar representation for the cylindrical spatial coordinates (R, theta, Z), a renormalized Fourier series moment expansion is obtained that possesses superior convergence properties in mode number space. This convergent spectral representation also determines a unique poloidal angle and thus resolves the underdetermined structure of previous moment expansions. A conformal mapping technique is used to demonstrate the existence and uniqueness of the new representation

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Oct 1984; 18 p; Available from NTIS, PC A02/MF A01 as DE85000866

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Hirshman, S.P.

Oak Ridge National Lab., TN (USA)

Oak Ridge National Lab., TN (USA)

AbstractAbstract

[en] A variational calculation of the current induced in a plasma by fast beam particles is presented. A new energy polynomial expansion of the classical Spitzer function is obtained and used to derive an accurate analytic expression for the beam-induced current j/sub parallel/, which includes the effects of electron-electron collisions and is valid for all values of anti v/sub b/ = v/sub b//v/sub e/ and effective charge anti Z. This analytic result is in excellent agreement with previous numerical calculations. An accurate rational form for the beam-induced current as a function of beam velocity is obtained by patching the large and small anti v/sub b/ asymptotic expansions of j/sub parallel/

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Dec 1979; 31 p; Available from NTIS., PC A03/MF A01

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Hirshman, S.P.

Oak Ridge National Lab., TN (USA)

Oak Ridge National Lab., TN (USA)

AbstractAbstract

[en] The basic properties of curvilinear coordinates are reviewed. Some applications to the description of three-dimensional magnetic confinement geometries are cited. The notation used here attempts to be consistent with the literature, and the relation to differential geometry is stressed

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Aug 1982; 25 p; Available from NTIS., PC A02/MF A01 as DE82019733

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Hirshman, S.P.

Princeton Univ., N.J. (USA). Plasma Physics Lab

Princeton Univ., N.J. (USA). Plasma Physics Lab

AbstractAbstract

[en] The classical parallel friction coefficients, which relate the collisional friction forces to the flow of particles and heat along the magnetic field, are calculated for a multiple ion species plasma. In the short mean free path regime, the neoclassical Pfirsch--Schlueter transport coefficients for a toroidally confined multispecies plasma are computed in terms of the classical friction coefficients. The dependence of the neoclassical cross-field transport on the equilibration of the parallel ion temperature profiles is determined

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Oct 1976; 48 p; Available from NTIS. $4.00.

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Hirshman, S.P.

Princeton Univ., N.J. (USA). Plasma Physics Lab

Princeton Univ., N.J. (USA). Plasma Physics Lab

AbstractAbstract

[en] The neoclassical cross-field fluxes for a toroidally confined, axisymmetric plasma are calculated in terms of the thermodynamic forces from the fluid continuity and momentum balance equations. This macroscopic formulation of neoclassical transport theory unifies the numerous complex expressions for the transport coefficients, previously obtained by solving the Fokker-Planck equation, and elucidates their physical basis. In the large aspect ratio limit, the continuous transition in the scaling of the diffusion coefficient throughout various collisionality regimes is shown to depend on the ratio of parallel viscosity coefficients of the plasma species. Comparison of the present results with the kinetic theory expressions for the neoclassical fluxes determines the parallel viscosity coefficients for a multispecies plasma in the long-mean-free-path regime

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Sep 1977; 25 p; Available from NTIS., PC A02/MF A01

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Hirshman, S.P.

Oak Ridge National Lab., TN (USA)

Oak Ridge National Lab., TN (USA)

AbstractAbstract

[en] The nonlinear motion of a charged particle in a uniformly magnetized, two-dimensional plasma is analyzed in the presence of finite amplitude electrostatic waves traveling in the plane perpendicular to the magnetic field. In a strongly magnetized plasma, no particle trapping occurs in a single electrostatic traveling wave of arbitrary amplitude, since the induced E Vector x B Vector motion is orthogonal to the direction of wave propagation. However, particle orbits can be trapped when there are at least two mutually orthogonal components of the electrostatic field with finite wave amplitude E/sub perpendicular/B greater than or equal to ω/k/sub perpendicular/ such that a particle drifts one wavelength in a wave period. This threshold amplitude for strong nonlinear behavior coincides with and helps to explain the many-wave turbulence criterion for the onset of particle diffusion in a two-dimensional plasma

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Aug 1979; 23 p; Available from NTIS., PC A02/MF A01

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Hirshman, S.P.; Meier, H.K.

Oak Ridge National Lab., TN (USA)

Oak Ridge National Lab., TN (USA)

AbstractAbstract

[en] The selection of an optimal parametric angle theta describing a closed magnetic flux surface is considered with regard to accelerating the convergence rate of the Fourier series for the Cartesian coordinates x(theta,phi) identical with R - R

_{0}and y(theta,phi) identical with Z - Z_{0}. Geometric criteria are developed based on the Hamiltonian invariants of Keplerian orbits. These criteria relate the rate of curve traversal (tangential speed) to the curvature (normal acceleration) so as to provide increased angular resolution in regions of largest curvature. They are, however, limited to either convex or starlike domains and do not provide rapid convergence for complex domains with alternating convex and concave regions. A generally applicable constraint criterion, based directly on minimizing the width of the x and y Fourier spectra, is also derived. A variational principle is given for implementing these constraints numerically. Application to the representation of three-dimensional magnetic flux surfaces is discussedPrimary Subject

Source

Nov 1984; 36 p; Available from NTIS, PC A03/MF A01; 1 as DE85003831

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Hirshman, S.P.; Molvig, K.

Oak Ridge National Lab., TN (USA)

Oak Ridge National Lab., TN (USA)

AbstractAbstract

[en] It is shown that the radial variation of the electron-to-ion temperature ratio induced by neutral beam injection in PLT could account for the observed spatial dependence of the electron thermal conductivity coefficient. Quantitative evaluations using the experimental temperature and electron thermal conductivity (chi/sub e/) profiles show consistency of the measured data with a finite beta drift wave turbulence model and also demonstrate the failure of a simple electron temperature power law scaling for chi/sub e/

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May 1981; 17 p; Available from NTIS., PC A02/MF A01

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Hirshman, S.P.; Boozer, A.H.

Princeton Univ., N.J. (USA). Plasma Physics Lab

Princeton Univ., N.J. (USA). Plasma Physics Lab

AbstractAbstract

[en] The parallel current in a toroidally-conformed plasma is shown to generally consist of the current in response to the parallel electric field, the Pfirsch-Schluter current which is required by charge neutrality, and the bootstrap current which flows to maintain a balance between the viscous and friction forces along the magnetic field. The steady-state momentum equation is solved to obtain an expression for the parallel current in terms of the electric field and the neoclassical cross-field fluxes of particles and heat in a multiple ion species plasma. It is found that the presence of impurities does not alter the magnitude of the bootstrap current. Thus, the neoclassical beta limit established by the bootstrap current is insensitive to the impurity content of the plasma. The magnitudes of the bootstrap current and conjugate Ware fluxes are investigated in the transition from the long mean-free path to collisional regime

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Dec 1977; 44 p; Available from NTIS., PC A03/MF A01

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Hirshman, S.P.; Lee, D.K.

Oak Ridge National Lab., TN (USA)

Oak Ridge National Lab., TN (USA)

AbstractAbstract

[en] A description is given of a new code, MOMCON (spectral moments with constraints), that obtains three-dimensional ideal magnetohydrodynamic (MHD) equilibria in a fixed toroidal domain using a Fourier expansion for the inverse coordinates (R,Z) representing nested magnetic surfaces. A set of nonlinear coupled ordinary differential equations for the spectral coefficients of (R,Z) is solved using an accelerated steepest descent method. A stream function lambda is introduced to improve the mode convergence properties of the Fourier series for R and Z. Constraint equations relating the m greater than or equal to 2 moments of R and Z are solved to define a unique poloidal angle

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Jul 1985; 35 p; Available from NTIS, PC A03/MF A01 as DE85015065

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