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Variational-moment method for computing magnetohydrodynamic equilibria

Description: A fast yet accurate method to compute magnetohydrodynamic equilibria is provided by the variational-moment method, which is similar to the classical Rayleigh-Ritz-Galerkin approximation. The equilibrium solution sought is decomposed into a spectral representation. The partial differential equations describing the equilibrium are then recast into their equivalent variational form and systematically reduced to an optimum finite set of coupled ordinary differential equations. An appropriate spectral decomposition can make the series representing the solution coverge rapidly and hence substantially reduces the amount of computational time involved. The moment method was developed first to compute fixed-boundary inverse equilibria in axisymmetric toroidal geometry, and was demonstrated to be both efficient and accurate. The method since has been generalized to calculate free-boundary axisymmetric equilibria, to include toroidal plasma rotation and pressure anisotropy, and to treat three-dimensional toroidal geometry. In all these formulations, the flux surfaces are assumed to be smooth and nested so that the solutions can be decomposed in Fourier series in inverse coordinates. These recent developments and the advantages and limitations of the moment method are reviewed. The use of alternate coordinates for decomposition is discussed.
Date: August 1, 1983
Creator: Lao, L.L.
Partner: UNT Libraries Government Documents Department

MHD Instabilities Occurring Near/AT the Transport Barrier, Including Loss of Confinement in H-Modes

Description: In configurations with transport barriers the improved edge and core confinement leads to large pressure gradient and large edge bootstrap current density which often drive magnetohydrodynamic (MHD) instabilities terminating the discharge or reducing the discharge performance. The edge and the core transport barriers deteriorate or are completely lost. In this presentation, recent experimental and theoretical developments concerning MHD instabilities occurring near/at the edge and the core transport barriers are summarized emphasizing the dominant instabilities and the comparison with theory.
Date: September 1, 1999
Creator: Lao, L. L.
Partner: UNT Libraries Government Documents Department

Developments in tokamak transport modeling

Description: A variety of numerical methods for solving the time-dependent fluid transport equations for tokamak plasmas is presented. Among the problems discussed are techniques for solving the sometimes very stiff parabolic equations for particle and energy flow, treating convection-dominated energy transport that leads to large cell Reynolds numbers, optimizing the flow of a code to reduce the time spent updating the particle and energy source terms, coupling the one-dimensional (1-D) flux-surface-averaged fluid transport equations to solutions of the 2-D Grad-Shafranov equation for the plasma geometry, handling extremely fast transient problems such as internal MHD disruptions and pellet injection, and processing the output to summarize the physics parameters over the potential operating regime for reactors. Emphasis is placed on computational efficiency in both computer time and storage requirements.
Date: January 1, 1981
Creator: Houlberg, W.A.; Attenberger & Lao, L.L.
Partner: UNT Libraries Government Documents Department

Stabilization of ballooning modes with sheared toroidal rotation

Description: A new code demonstrates the stabilization of MHD ballooning modes by sheared toroidal rotation. A shifted-circle model is used to elucidate the physics and numerically reconstructed equilibria are used to analyze DIII-D discharges. In the ballooning representation, the modes shift periodically along the field line to the next point of unfavorable curvature. The shift frequency (d{Omega}/dq where {Omega} is the angular toroidal velocity and q is the safety factor) is proportional to the rotation shear and inversely proportional to the magnetic shear. Stability improves with increasing shift frequency and, in the shifted circle model, direct stable access to the second stability regime occurs when this frequency is a fraction of the Alfven frequency {omega}{sub A} = V{sub A}/qR. Shear stabilization is also demonstrated for an equilibrium reconstruction of a DIII-D VH-mode.
Date: November 1, 1994
Creator: Miller, R.L.; Waelbroeck, F.W.; Lao, L.L. & Taylor, T.S.
Partner: UNT Libraries Government Documents Department

Effects of plasma shape and profiles on edge stability in DIII-D

Description: The results of recent experimental and theoretical studies concerning the effects of plasma shape and current and pressure profiles on edge instabilities in DIII-D are presented. Magnetic oscillations with toroidal mode number n {approx} 2--9 and a fast growth time {gamma}{sup {minus}1} = 20--150 {micro}s are often observed prior to the first giant type 1 ELM in discharges with moderate squareness. High n ideal ballooning second stability access encourages edge instabilities by facilitating the buildup of the edge pressure gradient and bootstrap current density which destabilize the intermediate to low n modes. Analysis suggests that discharges with large edge pressure gradient and bootstrap current density are more unstable to n > 1 modes. Calculations and experimental results show that ELM amplitude and frequency can be varied by controlling access to the second ballooning stability regime at the edge through variation of the squareness of the discharge shape. A new method is proposed to control edge instabilities by reducing access to the second ballooning stability regime at the edge using high order local perturbation of the plasma shape in the outboard bad curvature region.
Date: December 1, 1998
Creator: Lao, L.L.; Chan, V.S. & Chen, L.
Partner: UNT Libraries Government Documents Department

Demonstration of high performance negative central magnetic shear discharges on the DIII-D tokamak

Description: Reliable operation of discharges with negative central magnetic shear has led to significant increases in plasma performance and reactivity in both low confinement, L-mode, and high confinement, H-mode, regimes in the DIII-D tokamak. Using neutral beam injection early in the initial current ramp, a large range of negative shear discharges have been produced with durations lasting up to 3.2 s. The total non- inductive current (beam plus bootstrap) ranges from 50% to 80% in these discharges. In the region of shear reversal, significant peaking of the toroidal rotation [f{sub {phi}} {approx} 30-60 kHz] and ion temperature [T{sub i}(0) {approx} 15-22 keV] profiles are observed. In high power discharges with an L-mode edge, peaked density profiles are also observed. Confinement enhancement factors up to H {equivalent_to} {tau}{sub E}/{tau}{sub ITER-89P} {approx} 2.5 with an L-mode edge, and H {approx} 3.3 in an Edge Localized Mode (ELM)-free H-mode, are obtained. Transport analysis shows both ion thermal diffusivity and particle diffusivity to be near or below standard neoclassical values in the core. Large pressure peaking in L- mode leads to high disruptivity with {Beta}{sub N} {equivalent_to} {Beta}{sub T}/(I/aB) {<=} 2.3, while broader pressure profiles in H- mode gives low disruptivity with {Beta}{sub N} {<=} 4.2.
Date: January 1, 1996
Creator: Rice, B.W.; Burrell, K.H. & Lao, L.L.
Partner: UNT Libraries Government Documents Department

Rotational and magnetic shear stabilization of magnetohydrodynamic modes and turbulence in DIII-D high performance discharges

Description: The confinement and the stability properties of the DIII-D tokamak high performance discharges are evaluated in terms of rotational and magnetic shear with emphasis on the recent experimental results obtained from the negative central magnetic shear (NCS) experiments. In NCS discharges, a core transport barrier is often observed to form inside the NCS region accompanied by a reduction in core fluctuation amplitudes. Increasing negative magnetic shear contributes to the formation of this core transport barrier, but by itself is not sufficient to fully stabilize the toroidal drift mode (trapped- electron-{eta}{sub i}mode) to explain this formation. Comparison of the Doppler shift shear rate to the growth rate of the {eta}{sub i} mode suggests that the large core {bold E x B} flow shear can stabilize this mode and broaden the region of reduced core transport . Ideal and resistive stability analysis indicates the performance of NCS discharges with strongly peaked pressure profiles is limited by the resistive interchange mode to low {Beta}{sub N} {lt} 2.3. This mode is insensitive to the details of the rotational and the magnetic shear profiles. A new class of discharges which has a broad region of weak or slightly negative magnetic shear (WNS) is described. The WNS discharges have broader pressure profiles and higher values than the NCS discharges together with high confinement and high fusion reactivity.
Date: August 1, 1996
Creator: Lao, L.L.; Burrell, K.H. & Casper, T.S.
Partner: UNT Libraries Government Documents Department

Microinstability properties of negative magnetic shear discharges in the Tokamak Fusion Test Reactor and DIII-D

Description: The microinstability properties of discharges with negative (reversed) magnetic shear in the Tokamak Fusion Test Reactor (TFTR) and DIII-D experiments with and without confinement transitions are investigated. A comprehensive kinetic linear eigenmode calculation employing the ballooning representation is employed with experimentally measured profile data, and using the corresponding numerically computed magnetohydrodynamic (MHD) equilibria. The instability considered is the toroidal drift mode (trapped-electron-{eta}{sub i} mode). A variety of physical effects associated with differing q-profiles are explained. In addition, different negative magnetic shear discharges at different times in the discharge for TFTR and DIII-D are analyzed. The effects of sheared toroidal rotation, using data from direct spectroscopic measurements for carbon, are analyzed using comparisons with results from a two-dimensional calculation. Comparisons are also made for nonlinear stabilization associated with shear in E{sub r}/RB{sub {theta}}. The relative importance of changes in different profiles (density, temperature, q, rotation, etc.) on the linear growth rates is considered.
Date: March 1997
Creator: Rewoldt, G.; Tang, W. M. & Lao, L. L.
Partner: UNT Libraries Government Documents Department

Impact of edge current density and pressure gradient on the stability of DIII-D high performance discharges

Description: One of the major goals of advanced tokamak research is to develop plasma configurations with good confinement and improved stability at high {beta}. In DIII-D, various high performance configurations with H- and VH-mode edges have been produced. These include discharges with poloidal cross sections in the forms of dee and crecent shapes, single- and double-null divertors, and with various central magnetic shear profiles and current profile peakedness. All these discharges exhibit confinement in the outer plasma region which leads to a large edge pressure gradient and a large edge bootstrap current driven by this steep pressure gradient. These edge conditions often drive an instability near the edge region which can severely degrade the discharge performance. An understanding of this edge instability is essential to sustain an enhance discharge performance.
Date: June 1997
Creator: Lao, L. L.; Ferron, J. R. & Strait, E. J.
Partner: UNT Libraries Government Documents Department

IEFIT - An Interactive Approach to High Temperature Fusion Plasma Magnetic Equilibrium Fitting

Description: An interactive IDL based wrapper, IEFIT, has been created for the magnetic equilibrium reconstruction code EFIT written in FORTRAN. It allows high temperature fusion physicists to rapidly optimize a plasma equilibrium reconstruction by eliminating the unnecessarily repeated initialization in the conventional approach along with the immediate display of the fitting results of each input variation. It uses a new IDL based graphics package, GaPlotObj, developed in cooperation with Fanning Software Consulting, that provides a unified interface with great flexibility in presenting and analyzing scientific data. The overall interactivity reduces the process to minutes from the usual hours.
Date: June 1, 1999
Creator: Peng, Q.; Schachter, J.; Schissel, D.P. & Lao, L.L.
Partner: UNT Libraries Government Documents Department

Confinement and stability of DIII-D negative central shear discharges

Description: Negative central magnetic shear (NCS) discharges with {Beta}{sub N} {le} 4, H {le} 3, and up to 80% of the current non-inductively driven are reproducibly produced in the DIII-D tokamak. Strong peaking of T{sub i}, plasma rotation, and in some cases n{sub e} are observed inside the NCS region. Transport analysis shows that the core ion thermal diffusivity is substantially reduced and near the neoclassical value after the formation of the internal transport barrier. The negative central shear is necessary but not sufficient for the formation of this transport barrier. The power required for the formation appears to increase with the toroidal magnetic field. The high performance phase of H-mode NCS discharges often ends with an ELM-like collapse initiated from the edge whereas the L-mode discharges which have a more peaked pressure profile tend to end with a more global n = 1 MHD event.
Date: December 1, 1995
Creator: Lao, L.L.; Burrell, K.H. & Chan, V.S.
Partner: UNT Libraries Government Documents Department

The effect of current profile changes on confinement in the DIII-D tokamak

Description: Experiments in the DIII-D tokamak have demonstrated that the effect of changes in the current profile on plasma confinement varies with the discharge shape. The results are similar in many respects to those from other tokamaks. In all cases, a rapid change in the plasma current in an L-mode, circular or moderately elongated, discharge has been used to produce a transient change in the current density profile. Although the detailed results vary among tokamaks, it is generally observed that during and immediately following a negative plasma current ramp, the stored energy does not follow the L-mode scaling that predicts that confinement should be proportional to the total plasma current. The stored energy changes on the time scale of the relaxation of the current density profile rather than the shorter time scales of the energy confinement time or the change in the total current. Because of the discharge having capability of the DIII-K tokamak it has been possible to extend these current ramp experiments beyond the L-mode, moderate elongation case to highly elongated double-null divertor discharges in H-mode. In separate experiments, a rapid change in the discharge elongation has also been used to vary the current density profile. This paper shows that the dependence of the plasma confinement on the current profile changes when the discharge shape is changed. This variation with discharge shape provides evidence for a model that predicts that changes in the local magnetic shear resulting from the changes in the current profile can result in decreased local transport.
Date: May 1, 1992
Creator: Ferron, J. R.; Lao, L. L. & Taylor, T. S.
Partner: UNT Libraries Government Documents Department


Description: Edge localized modes (ELMs) are commonly observed in high energy confinement, tokamak plasmas and are thought to be caused by magnetohydrodynamic instabilities driven by the steep pressure gradient and the current in the plasma edge region. Our data show that the divertor magnetic balance, i.e., the degree to which the plasma topology resembles a single-null (SN) or a double-null (DN), strongly determines where particle pulses driven by ballooning instabilities at the plasma edge are distributed to surrounding vacuum vessel surfaces. These data also support the conclusions drawn from the stability analysis that ELMs are generated almost entirely on the outboard side of the main plasma.
Date: June 1, 2002
Creator: PETRIE, T.W.; WATKINS, J.G.; LAO, L.L. & SNYDER, P.B.
Partner: UNT Libraries Government Documents Department

The importance of the radial electric field (E{sub r}) on interpretation of motional Stark effect measurements of the q profile in DIII-D high performance plasmas

Description: The development of enhanced confinement regimes such as negative central magnetic shear (NCS) and VH-mode illustrates the importance of the q profile and ExB velocity shear in improving stability and confinement in tokamak plasmas. Recently, it was realized that the large values of radial electric field observed in these high performance plasmas, up to 200 kV/m in DIII-D, have an effect on the interpretation of motional Stark effect (MSE) measurements of the q profile. It has also been shown that, with additional MSE measurements, one can extract a direct measurement of E{sub r} in addition to the usual poloidal field measurement. During a recent vent on DIII-D, 19 additional MSE channels with new viewing angles were added (for a total of 35 channels) in order to descriminate between the neutral beam v{sub b} x B electric field and the plasma E{sub r} field. In this paper, the system upgrade will be described and initial measurements demonstrating simultaneous measurement of the q and E{sub r} profiles will be presented.
Date: June 1, 1997
Creator: Rice, B.W.; Lao, L.L.; Burrell, K.H.; Greenfield, C.M. & Lin-Liu, Y.R.
Partner: UNT Libraries Government Documents Department

DIII-D Advanced Tokamak Research Overview

Description: This paper reviews recent progress in the development of long-pulse, high performance discharges on the DIII-D tokamak. It is highlighted by a discharge achieving simultaneously {beta}{sub N}H of 9, bootstrap current fraction of 0.5, noninductive current fraction of 0.75, and sustained for 16 energy confinement times. The physics challenge has changed in the long-pulse regime. Non-ideal MHD modes are limiting the stability, fast ion driven modes may play a role in fast ion transport which limits the stored energy and plasma edge behavior can affect the global performance. New control tools are being developed to address these issues.
Date: December 1, 1999
Creator: Chan, V.S.; Greenfield, C.M.; Lao, L.L.; Luce, T.C.; Petty, C.C. & Staebler, G.M.
Partner: UNT Libraries Government Documents Department

Observation of SOL Current Correlated with MHD Activity in NBI-heated DIII-D Tokamak Discharges

Description: This work investigates the potential roles played by the scrape-off-layer current (SOLC) in MHD activity of tokamak plasmas, including effects on stability. SOLCs are found during MHD activity that are: (1) slowly growing after a mode-locking-like event, (2) oscillating in the several kHz range and phase-locked with magnetic and electron temperature oscillations, (3) rapidly growing with a sub-ms time scale during a thermal collapse and a current quench, and (4) spiky in temporal behavior and correlated with spiky features in Da signals commonly identified with the edge localized mode (ELM). These SOLCs are found to be an integral part of the MHD activity, with a propensity to flow in a toroidally non-axisymmetric pattern and with magnitude potentially large enough to play a role in the MHD stability. Candidate mechanisms that can drive these SOLCs are identified: (a) toroidally non-axisymmetric thermoelectric potential, (b) electromotive force (EMF) from MHD activity, and (c) flux swing, both toroidal and poloidal, of the plasma column. An effect is found, stemming from the shear in the field line pitch angle, that mitigates the efficacy of a toroidally non-axisymmetric SOLC to generate a toroidally non-axisymmetric error field. Other potential magnetic consequences of the SOLC are identified: (i) its error field can introduce complications in feedback control schemes for stabilizing MHD activity and (ii) its toroidally non-axisymmetric field can be falsely identified as an axisymmetric field by the tokamak control logic and in equilibrium reconstruction. The radial profile of a SOLC observed during a quiescent discharge period is determined, and found to possess polarity reversals as a function of radial distance.
Date: March 26, 2004
Creator: Takahashi, H.; Fredrickson, E.D.; Schaffer, M.J.; Austin, M.E.; Evans, T.E.; Lao, L.L. et al.
Partner: UNT Libraries Government Documents Department


Description: Electron cyclotron current drive (ECCD) experiments on the DIII-D tokamak are solidifying the physics basis for localized, off-axis current drive, the goal being to validate a predictive model for ECCD. The ECCD profiles are determined from the magnetic field pitch angles measured by motional Stark effect (MSE) polarimetry. The measured ECCD switches from the co to the counter direction as the toroidal injection angle is varied with a profile width that is in accordance with ray tracing calculations. Tests of electron trapping in low beta plasmas show that the ECCD efficiency decreases rapidly as the deposition is moved off-axis and towards the outboard side of the plasma, but the detrimental effects of electron trapping on the current drive are greatly reduced in high beta plasmas. Overall, the measured ECCD is in good agreement with theoretical calculations using a quasilinear Fokker-Planck code over a wide range of injection angles and plasma parameters.
Date: May 1, 2002
Creator: PETTY, C.C.; PRATER, R.; LOHR, J.; LUCE, T.C.; FOX,W.R.; HARVEY, R.W. et al.
Partner: UNT Libraries Government Documents Department

Stability of TAE modes in DIII-D

Description: TAE modes driven by neutral beam injection have been observed in DIII-D. The measured frequency agrees very well with theoretical predictions for DIII-D discharges. At large amplitude these instabilities can lead to loss of over 50% of the beam power, as well as large loss of non-resonant MeV fusion products. The threshold value of fast ion beta for destabilization and the observed range of unstable mode numbers are in reasonable agreement with predictions for the mode growth rate. Continuum damping dominates at low mode numbers, while damping by electron kinetic effects dominates at high mode numbers. Preliminary experiments suggest that TAB modes can be stabilized by current profile control.
Date: September 1, 1992
Creator: Strait, E. J.; Chu, M. S.; Lao, L. L.; Turnbull, A. D.; Heidbrink, W. W. & Duong, H. H.
Partner: UNT Libraries Government Documents Department

Coupled MHD and transport analysis of improved confinement DIII-D discharges

Description: Transiently high internal inductance discharges are used to check the validity of evolvement of current profiles obtained with the MHD/transport coupled scheme presented below. Both a current ramp and an elongation ramp discharge are examined. To simulate energy confinement the Rebut-Lallia-Watkins model is used for the current ramp discharge. In our simulation of experimental discharges external circuit behavior is accounted for by using measured, time dependent, flux loops, magnetic probes, field shaping and ohmic coil currents. The small effect of eddy currents in the plasma vessel are neglected. We use measured, time dependent electron and ion temperature profiles, electron density, Z{sub eff}, toroidal rotation and radiated power profiles to constrain our analyses. For the RLW simulation measured values of T{sub e} and T{sub i} at the plasma edge are used as boundary conditions in the electron and ion energy equations.
Date: May 1, 1993
Creator: St. John, H.; Ferron, J. R.; Lao, L. L.; Osborne, T. H.; Thompson, S. J. & Wroblewski, D.
Partner: UNT Libraries Government Documents Department


Description: During 1998, the General Atomics (GA) ARIES-Spherical Torus (ST) team examined several critical issues related to the physics performance of the ARIES-ST design, and a number of suggestions were made concerning possible improvements in performance. These included specification of a reference plasma equilibrium, optimization about the reference equilibrium to achieve higher beta limits, examination of three possible schemes for plasma initiation, development of a detailed scenario for ramp-up of the plasma current and pressure to its full, final operating values, an assessment of the requirement for electron confinement, and several suggestions for divertor heat flux reduction. The reference equilibrium was generated using the TOQ code, with the specification of a 100%, self-consistent bootstrap current. The equilibrium has {beta} = 51%, 10% below the stability limit (a margin specified by the ARIES-ST study). In addition, a series of intermediate equilibria were defined, corresponding to the ramp-up scenario discussed. A study of the influence of shaping on ARIES-ST performance indicates that significant improvement in both kink and ballooning stability can be obtained by modest changes in the squareness of the plasma. In test equilibria the ballooning beta limit is increased from 58% to 67%. Also the maximum allowable plasma-wall separation for kink stability can be increased by 30%. Three schemes were examined for noninductive plasma initiation. These are helicity injection (HICD), electron cyclotron heating (ECH)-assisted startup, and inductive startup using only the external equilibrium coils. HICD startup experiments have been done on the HIT and CDX devices. ECH-assisted startup has been demonstrated on CDX-U and DIII-D. External coil initiation is based on calculations for a proposed DIII-D experiment. In all cases, plasma initiation and preparation of an approximately 0.3 MA plasma for ARIES-ST appears entirely feasible.
Date: April 1, 1999
Creator: CHAN, V.S.; LAO, L.L.; LIN-LIU, Y.R.; MILLER, R.L.; PETRIE, T.W.; POLITZER, P.A. et al.
Partner: UNT Libraries Government Documents Department

Non-Inductive Current Drive Modeling Extending Advanced Tokamak Operation to Steady State

Description: A critical issue for sustaining high performance, negative central shear (NCS) discharges is the ability to maintain current distributions that are maximum off axis. Sustaining such hollow current profiles in steady state requires the use of non-inductively driven current sources. On the DIII-D experiment, a combination of neutral beam current drive (NBCD) and bootstrap current have been used to create transient NCS discharges. The electron cyclotron heating (ECH) and current drive (ECCD) system is currently being upgraded from three gyrotrons to six to provide more than 3MW of absorbed power in long-pulse operation to help sustain the required off-axis current drive. This upgrade SuPporrs the long range goal of DIII-D to sustain high performance discharges with high values of normalized {beta}, {beta}{sub n} = {beta}/(I{sub p}/aB{sub T}), confinement enhancement factor, H, and neutron production rates while utilizing bootstrap current fraction, f{sub bs}, in excess of 50%. At these high performance levels, the likelihood of onset of MHD modes that spoil confinement indicates the need to control plasma profiles if we are to extend this operation to long pulse or steady state. To investigate the effectiveness of the EC system and to explore operating scenarios to sustain these discharges, we use time-dependent simulations of the equilibrium, transport and stability. We explore methods to directly alter the safety factor profile, q, through direct current drive or by localized electron heating to modify the bootstrap current profile. Time dependent simulations using both experimentally determined [1] and theory-based [2] energy transport models have been done. Here, we report on simulations exploring parametric dependencies of the heating, current drive, and profiles that affect our ability to sustain stable discharges.
Date: June 6, 2000
Creator: Casper, T.A.; Lodestro, L.L.; Pearlstein, L.D.; Porter, G.D.; Murakami, M.; Lao, L.L. et al.
Partner: UNT Libraries Government Documents Department

Wall stabilization of high beta plasmas in DIII-D

Description: Detailed analysis of recent high beta discharges in the DIII-D tokamak demonstrates that the resistive vacuum vessel can provide stabilization of low n magnetohydrodynamic (MHD) modes. The experimental beta values reaching up to {beta}{sub T} = 12.6% are more than 30% larger than the maximum stable beta calculated with no wall stabilization. Plasma rotation is essential for stabilization. When the plasma rotation slows sufficiently, unstable modes with the characteristics of the predicted {open_quotes}resistive wall{close_quotes} mode are observed. Through slowing of the plasma rotation between the q = 2 and q = 3 surfaces with the application of a non-axisymmetric field, the authors have determined that the rotation at the outer rational surfaces is most important, and that the critical rotation frequency is of the order of {Omega}/2{pi} = 1 kHz.
Date: February 1, 1995
Creator: Taylor, T.S.; Strait, E.J.; Lao, L.L.; Turnbull, A.D.; Burrell, K.H.; Chu, M.S. et al.
Partner: UNT Libraries Government Documents Department