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Neoclassical tearing modes in a tokamak

Description: Linear tearing instability is studied in the banana collisionality regime in tokamak geometry. Neoclassical effects produce significant modifications of Ohm's law and the vorticity equation so that the growth rate of tearing modes driven by ..delta..' is dramatically reduced compared to the usual resistive MHD value. Consequences of this result, regarding the presence of pressure-gradient-driven neoclassical resistive interchange instabilities and the evolution of magnetic islands in the Rutherford regime, are discussed. 10 refs.
Date: August 1, 1988
Creator: Hahm, T.S.
Partner: UNT Libraries Government Documents Department

Theory of semicollisional drift-interchange modes in cylindrical plasmas

Description: Resistive interchange instabilities in cylindrical plasmas are studied, including the effects of electron diamagnetic drift, perpendicular resistivity, and plasma compression. The analyses are pertinent to the semicollisional regime where the effective ion gyro-radius is larger than the resistive layer width. Both analytical and numerical results show that the modes can be completely stabilized by the perpendicular plasma transport. Ion sound effects, meanwhile, are found to be negligible in the semicollisional regime.
Date: January 1, 1985
Creator: Hahm, T.S. & Chen, L.
Partner: UNT Libraries Government Documents Department

Theory of semicollisional kinetic Alfven modes in sheared magnetic fields

Description: The spectra of the semicollisional kinetic Alfven modes in a sheared slab geometry are investigated, including the effects of finite ion Larmor radius and diamagnetic drift frequencies. The eigenfrequencies of the damped modes are derived analytically via asymptotic analyses. In particular, as one reduces the resistivity, we find that, due to finite ion Larmor radius effects, the damped mode frequencies asymptotically approach finite real values corresponding to the end points of the kinetic Alfven continuum.
Date: February 1, 1985
Creator: Hahm, T.S. & Chen, L.
Partner: UNT Libraries Government Documents Department

Nonlinear theory of trapped electron temperature gradient driven turbulence in flat density H-mode plasmas

Description: Ion temperature gradient turbulence based transport models have difficulties reconciling the recent DIII-D H-mode results where the density profile is flat, but {chi}{sub e} > {chi}{sub i} in the core region. In this work, a nonlinear theory is developed for recently discovered ion temperature gradient trapped electron modes propagating in the electron diamagnetic direction. This instability is predicted to be linearly unstable for L{sub Ti}/R {approx lt} {kappa}{sub {theta}}{rho}{sub s} {approx lt} (L{sub Ti}/R){sup 1/4}. They are also found to be strongly dispersive even at these long wavelengths, thereby suggesting the importance of the wave-particle-wave interactions in the nonlinear saturation phase. The fluctuation spectrum and anomalous fluxes are calculated. In accordance with the trends observed in DIII-D, the predicted electron thermal diffusivity can be larger than the ion thermal diffusivity. 17 refs., 3 figs.
Date: December 1, 1990
Creator: Hahm, T.S.
Partner: UNT Libraries Government Documents Department

Forced magnetic reconnection

Description: By studying a simple model problem, we examine the time evolution of magnetic field islands which are induced by perturbing the boundary surrounding an incompressible plasma with a resonant surface inside. We find that for sufficiently small boundary perturbations, the reconnection and island formation process occurs on the tearing mode time scale defined by Furth, Killeen, and Rosenbluth. For larger perturbations the time scale is that defined by Rutherford. The resulting asymptotic equilibrium is such that surface currents in the resonant region vanish. A detailed analytical picture of this reconnection process is presented.
Date: November 1, 1984
Creator: Hahm, T.S. & Kulsrud, R.M.
Partner: UNT Libraries Government Documents Department

Flow shear induced Compton scattering of electron drift instability

Description: Plasma flow shear effects on nonlinear saturation of electron drift waves are analyzed in the weak turbulence regime. Flow shear can enhance ion Compton scattering of long wavelength electron drift waves not only by modifying the beat wave-ion resonance condition, but also via the radial dependence of linear susceptibility. A nonlinear dispersion relation is obtained as a solution of the radially nonlocal nonlinear eigenmode equation. At nonlinear saturation, the spectral intensity of the fluctuations scales with flow shear as ({partial derivative}V{var phi}/{partial derivative}r){sup {minus}2} in addition to the linear dependence on the linear growth rate.
Date: February 1, 1992
Creator: Hahm, T.S.
Partner: UNT Libraries Government Documents Department

Trapped particle dynamics in toroidally rotating plasmas

Description: A detailed single particle orbit analysis is toroidally rotating plasma yields new analytical formulas for the second adiabatic invariant, the bounce frequency, and the precession frequency up to the first order correction in {rho}{sub pi}(poloidal ion gyroradium)/L{sub v}(scale length of rotation velocity), for toroidal flow values of the order of ion thermal velocity. Toroidal plasma rotation effects on the trapped ion instabilities in tokamaks are investigated in the context of local theory. Toroidal plasma rotation increases both the fraction of trapped particles and their precession drift velocity. Consequently, the growth rate of trapped ion instability increases in both dissipative and collisionless regimes.
Date: June 1, 1992
Creator: Hahm, T.S.
Partner: UNT Libraries Government Documents Department

Atomic physics effects on tokamak edge drift-tearing modes

Description: The effects of ionization and charge exchange on the linear stability of drift-tearing modes are analytically investigated. In particular, the linear instability threshold [Delta][sup Th], produced by ion sound wave coupling is modified. In the strongly collisional regime, the ionization breaks up the near cancellation of the perturbed electric field and the pressure gradient along the magnetic field, and increases the threshold. In the semi-collisional regime, both ionization and charge exchange act as drag on the ion parallel velocity, and consequently decrease the threshold by reducing the effectiveness of ion sound wave propagation.
Date: March 1, 1993
Creator: Hahm, T.S.
Partner: UNT Libraries Government Documents Department

Properties of ion temperature gradient drift instabilities in H-mode plasmas

Description: Experimental results from tokamaks such as DIII-D and JET have indicated that the electron density profile in H-mode (''high- confinement'') discharges can be nearly flat over most of the plasma, and, in some cases, even inverted (outwardly peaked). These conditions have very interesting implications for pictures of anomalous thermal transport based on the presence of ion temperature gradient drift instabilities. The present paper includes a new derivation of the ion temperature gradient threshold for weak density gradient /eta//sub i/ modes when ion transit resonances are taken into account; and the first derivation of threshold conditions for the onset of /eta//sub i/-modes when /eta//sub i/ is negative along with the properties of these negative /eta//sub i/ instabilities when the thresholds are exceeded. Possible consequences for confinement in H-mode plasmas are discussed. 32 refs., 8 figs.
Date: November 1, 1988
Creator: Hahm, T.S. & Tang, W.M.
Partner: UNT Libraries Government Documents Department

Atomic physics effects on tokamak edge drift-tearing modes

Description: The effects of ionization and charge exchange on the linear stability of drift-tearing modes are analytically investigated. In particular, the linear instability threshold {Delta}{sup Th}, produced by ion sound wave coupling is modified. In the strongly collisional regime, the ionization breaks up the near cancellation of the perturbed electric field and the pressure gradient along the magnetic field, and increases the threshold. In the semi-collisional regime, both ionization and charge exchange act as drag on the ion parallel velocity, and consequently decrease the threshold by reducing the effectiveness of ion sound wave propagation.
Date: March 1, 1993
Creator: Hahm, T. S.
Partner: UNT Libraries Government Documents Department

Flow shear induced Compton scattering of electron drift instability

Description: Plasma flow shear effects on nonlinear saturation of electron drift waves are analyzed in the weak turbulence regime. Flow shear can enhance ion Compton scattering of long wavelength electron drift waves not only by modifying the beat wave-ion resonance condition, but also via the radial dependence of linear susceptibility. A nonlinear dispersion relation is obtained as a solution of the radially nonlocal nonlinear eigenmode equation. At nonlinear saturation, the spectral intensity of the fluctuations scales with flow shear as ({partial_derivative}V{var_phi}/{partial_derivative}r){sup {minus}2} in addition to the linear dependence on the linear growth rate.
Date: February 1, 1992
Creator: Hahm, T. S.
Partner: UNT Libraries Government Documents Department

Trapped particle dynamics in toroidally rotating plasmas

Description: A detailed single particle orbit analysis is toroidally rotating plasma yields new analytical formulas for the second adiabatic invariant, the bounce frequency, and the precession frequency up to the first order correction in {rho}{sub pi}(poloidal ion gyroradium)/L{sub v}(scale length of rotation velocity), for toroidal flow values of the order of ion thermal velocity. Toroidal plasma rotation effects on the trapped ion instabilities in tokamaks are investigated in the context of local theory. Toroidal plasma rotation increases both the fraction of trapped particles and their precession drift velocity. Consequently, the growth rate of trapped ion instability increases in both dissipative and collisionless regimes.
Date: June 1, 1992
Creator: Hahm, T. S.
Partner: UNT Libraries Government Documents Department

Influence of radial electric field on Alfven-type instabilities

Description: The influence of the large scale radial electric field, E{sub r}{sup (0)} on the frequency of shear-Alfven-type instability is analyzed. A frozen-in-flux constraint and the moderate-{beta} ion gyrokinetic equation are used in the derivation. The analysis indicates that the frequency predicted by a theory with E{sub r}{sup (0)} effect should be Doppler-shifted by k {center_dot} V{sub E} for comparison to the experimentally observed frequency. A specific example of the practical relevance of the result is given regarding possible identification of the edge-localized-mode-associated magnetic activity recently observed in PBX-M tokamak experiment.
Date: March 1, 1994
Creator: Hahm, T.S. & Tang, W.M.
Partner: UNT Libraries Government Documents Department

On the dynamics of turbulent transport near marginal stability

Description: A general methodology for describing the dynamics of transport near marginal stability is formulated. Marginal stability is a special case of the more general phenomenon of self-organized criticality. Simple, one field models of the dynamics of tokamak plasma self-organized criticality have been constructed, and include relevant features such as sheared mean flow and transport bifurcations. In such models, slow mode (i.e. large scale, low frequency transport events) correlation times determine the behavior of transport dynamics near marginal stability. To illustrate this, impulse response scaling exponents (z) and turbulent diffusivities (D) have been calculated for the minimal (Burgers) and sheared flow models. For the minimal model, z = 1 (indicating ballastic propagation) and D {approximately}(S{sub 0}{sup 2}){sup 1/3}, where S{sub 0}{sup 2} is the noise strength. With an identically structured noise spectrum and flow with shearing rate exceeding the ambient decorrelation rate for the largest scale transport events, diffusion is recovered with z = 2 and D {approximately} (S{sub 0}{sup 2}){sup 3/5}. This indicates a qualitative change in the dynamics, as well as a reduction in losses. These results are consistent with recent findings from {rho} scaling scans. Several tokamak transport experiments are suggested.
Date: March 1, 1995
Creator: Diamond, P.H. & Hahm, T.S.
Partner: UNT Libraries Government Documents Department

E x B shearing rate in quasi-symmetric plasmas

Description: The suppression of turbulence by the E x B shear is studied in systems with quasi-symmetry using the nonlinear analysis of eddy decorrelation previously utilized in finite aspect ratio tokamak plasmas. The analytically derived E x B shearing rate which contains the relevant geometric dependence can be used for quantitative assessment of the fluctuation suppression in stellarators with quasi-symmetry.
Date: June 20, 1997
Creator: Hahm, T.S.
Partner: UNT Libraries Government Documents Department

Nonlinear theory of collisionless trapped ion modes

Description: A simplified two field nonlinear model for collisionless trapped-ion-mode turbulence has been derived from nonlinear bounce-averaged drift kinetic equations. The renormalized thermal diffusivity obtained from this analysis exhibits a Bohm-like scaling. A new nonlinearity associated with the neoclassical polarization density is found to introduce an isotope-dependent modification to this Bohm-like diffusivity. The asymptotic balance between the equilibrium variation and the finite banana width induced reduction of the fluctuation potential leads to the result that the radial correlation length decreases with increasing plasma current. Other important conclusions from the present analysis include the predictions that (i) the relative density fluctuation level {delta}n/n{sub 0} is lower than the conventional mixing length estimate, {Delta}r/L{sub n} (ii) the ion temperature fluctuation level {delta}T{sub i}/T{sub i} significantly exceeds the density fluctuation level {delta}n/n{sub 0}; and (iii) the parallel ion velocity fluctuation level {delta}v{sub i}{sub {parallel}}/v{sub Ti} is expected to be negligible.
Date: March 1, 1996
Creator: Hahm, T.S. & Tang, W.M.
Partner: UNT Libraries Government Documents Department

Role of flow shear in enhanced core confinement regimes

Description: The importance of the ExB flow shear in various enhanced confinement regimes is discussed in terms of the turbulence suppression criterion in toroidal geometry. This criterion is then further generalized to include the poloidal angle dependence of the equilibrium electrostatic potential. The implication of the recently observed in-out asymmetry in the fluctuation behavior in DIII-D VH-mode is discussed.
Date: March 1, 1996
Creator: Hahm, T.S. & Burrell, K.H.
Partner: UNT Libraries Government Documents Department

Nonlinear gyrokinetic theory for finite-BETA plasmas

Description: A self-consistent and energy-conserving set of nonlinear gyrokinetic equations, consisting of the averaged Vlasov and Maxwell's equations for finite-..beta.. plasmas, is derived. The method utilized in the present investigation is based on the Hamiltonian formalism and Lie transformation. The resulting formation is valid for arbitrary values of k/perpendicular//rho//sub i/ and, therefore, is most suitable for studying linear and nonlinear evolution of microinstabilities in tokamak plasmas as well as other areas of plasma physics where the finite Larmor radius effects are important. Because the underlying Hamiltonian structure is preserved in the present formalism, these equations are directly applicable to numerical studies based on the existing gyrokinetic particle simulation techniques. 31 refs.
Date: February 1, 1988
Creator: Hahm, T.S.; Lee, W.W. & Brizard, A.
Partner: UNT Libraries Government Documents Department

Linear stability of tearing modes

Description: This paper examines the stability of tearing modes in a sheared slab when the width of the tearing layer is much smaller than the ion Larmor radius. The ion response is nonlocal, and the quasineutrality retains its full integal form. An expansion procedure is introduced to solve the quasineutrality equation in powers of the width of the tearing layer over the ion Larmor radius. The expansion procedure is applied to the collisionless and semi-collisional tearing modes. The first order terms in the expansion we find to be strongly stabilizing. The physics of the mode and of the stabilization is discussed. Tearing modes are observed in experiments even though the slab theory predicts stability. It is proposed that these modes grow from an equilibrium with islands at the rational surfaces. If the equilibrium islands are wider than the ion Larmor radius, the mode is unstable when ..delta..' is positive.
Date: May 1, 1986
Creator: Cowley, S.C.; Kulsrud, R.M. & Hahm, T.S.
Partner: UNT Libraries Government Documents Department

Atomic physics effects on dissipative toroidal drift wave stability

Description: The effects of atomic physics processes such as ionization, charge exchange, and radiation on the linear stability of dissipative drift waves are investigated in toroidal geometry both numerically and analytically. For typical TFTR and TEXT edge parameters, overall linear stability is determined by the competition between the destabilizing influence of ionization and the stabilizing effect due to the electron temperature gradient. An analytical expression for the linear marginal stability condition, {eta}{sub e}{sup crit}, is derived. The instability is most likely to occur at the extreme edge of tokamaks with a significant ionization source and a steep electron density gradient.
Date: February 1, 1992
Creator: Beer, M.A. & Hahm, T.S.
Partner: UNT Libraries Government Documents Department

Weak turbulence theory of collisionless trapped electron driven drift instability in tokamaks

Description: The toroidal collisionless trapped electron modes are analyzed in the weak turbulence regime treating both ions and trapped electrons nonlinearly in the presence of ion and electron temperature gradients. The spectral intensity of the density fluctuations in the nonlinearly saturated state is analytically obtained from the steady state solution of the wave-kinetic equation. Distant nonlinear interactions between low-k{sub {theta}} and high-k{sub {theta}} modes of similar frequencies via trapped electron scattering (the resonance between the beat wave and the trapped electron precession drift frequencies) suppress the low-k{sub {theta}} (k{sub {theta}}{rho}{sub s} {much lt} (L{sub n}/R){sup 1/2}) modes while close interactions via ion Compton scattering (nonlinear ion Landau damping) produce a monotonically decreasing spectrum from k{sub {theta}}{rho}{sub s} {congruent} (L{sub n}/R){sup 1/2} to k{sub {theta}}{rho}{sub s} {congruent} 1 according to an approximate power law k{sub {theta}}{sup {minus}3}. Various fluctuation amplitudes at saturation and the fluctuation-induced anomalous particle and heat fluxes are found to be smaller than the mixing length estimates. The plasma confinement is predicted to improve with higher T{sub i}/T{sub e}, more peaked density profile, larger aspect ratio, and higher plasma current. Also, a significant dependence of transport on the electron temperature gradient is found which could contribute to the rigidity of the electron temperature profile often experimentally observed.
Date: October 1, 1990
Creator: Hahm, T.S. & Tang, W.M.
Partner: UNT Libraries Government Documents Department

Flow shear induced fluctuation suppression in finite aspect ratio shaped tokamak plasma

Description: The suppression of turbulence by the E {times} B flow shear and parallel flow shear is studied in an arbitrary shape finite aspect ratio tokamak plasma using the two point nonlinear analysis previously utilized in a high aspect rat& tokamak plasma. The result shows that only the E {times} B flow shear is responsible for the suppression of flute-like fluctuations. This suppression occurs regardless of the plasma rotation direction and is therefore, relevant for the VH mode plasma core as well as for the H mode plasma edge. Experimentally observed in-out asymmetry of fluctuation reduction behavior can be addressed in the context of flux expansion and magnetic field pitch variation on a given flux surface. The adverse effect of neutral particles on confinement improvement is also discussed in the context of the charge exchange induced parallel momentum damping.
Date: January 1, 1995
Creator: Hahm, T. S. & Burrell, K. H.
Partner: UNT Libraries Government Documents Department

Atomic physics effects on dissipative toroidal drift wave stability

Description: The effects of atomic physics processes such as ionization, charge exchange, and radiation on the linear stability of dissipative drift waves are investigated in toroidal geometry both numerically and analytically. For typical TFTR and TEXT edge parameters, overall linear stability is determined by the competition between the destabilizing influence of ionization and the stabilizing effect due to the electron temperature gradient. An analytical expression for the linear marginal stability condition, {eta}{sub e}{sup crit}, is derived. The instability is most likely to occur at the extreme edge of tokamaks with a significant ionization source and a steep electron density gradient.
Date: February 1, 1992
Creator: Beer, M. A. & Hahm, T. S.
Partner: UNT Libraries Government Documents Department

Fully Electromagnetic Nonlinear Gyrokinetic Equations for Tokamak Edge Turbulence

Description: An energy conserving set of the fully electromagnetic nonlinear gyrokinetic Vlasov equation and Maxwell's equations, which is applicable to both L-mode turbulence with large amplitude and H-mode turbulence in the presence of high E Χ B shear has been derived. The phase-space action variational Lie perturbation method ensures the preservation of the conservation laws of the underlying Vlasov-Maxwell system. Our generalized ordering takes ρ[sub ]i [\sub]<< ρϑ¡ ~ LE ~ Lp << R (here ρ[sub ]i [\sub] is the thermal ion Larmor radius and ρϑ¡ = [B over Bϑ] ρ[sub ]i [\sub]), as typically observed in the tokamak H-mode edge, with LE and Lp being the radial electric field and pressure gradient lengths. We take κ[sub ] perpendicular to[/sub] ρ[sub ]i [\sub] ~ 1 for generality, and keep the relative fluctuation amplitudes eδφ ⁄ Τ[sub ]i [\sub]~ δΒ ⁄ Β up to the second order. Extending the electrostatic theory in the presence of high E Χ B shear [Hahm, Phys. Plasmas 3, 4658 (1996)], contributions of electromagnetic fluctuations to the particle charge density and current are explicitly evaluated via pull-back transformation from the gyrocenter distribution function in the gyrokinetic Maxwell's equation.
Date: August 27, 2008
Creator: Hahm, T.S.; Wang, Lu, & Madsen, J.
Partner: UNT Libraries Government Documents Department