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ECRH in tandem mirror machines

Description: The thermal barrier concept and the use of ECRH to generate the several electron populations required to establish confinement are discussed. Important physics issues related to the microwave heating are discussed. Fokker-Planck calculations which model the heating processes are presented, followed by recent experimental data on hot electron heating.
Date: May 27, 1983
Creator: Stallard, B.W.
Partner: UNT Libraries Government Documents Department

Experiments on hot-electron ECRH in the Tandem Mirror Experiment-Upgrade

Description: Experiments have begun on the Tandem Mirror Experiment Upgrade (TMX-U) using electron-cyclotron resonant heating (ECRH) to generate the hot electron populations required for thermal barrier operation (Energy E/sub eh/ approx. 50 keV, density n/sub eh/ < 5 x 10/sup 12/, and hot-to-cold fraction n/sub eh/n approx. 0.9). For this operation, rf power produced by 28-GHz gyrotrons is injected with extraordinary mode polarization at both fundamental and second harmonic locations. Our initial experiments, which concentrated on startup of the hot electrons, were carried out at low density (< 1 x 10/sup 12/ cm/sup -3/) where Fokker-Planck calculations predict high heating efficiency when the electron temperature (T/sub e/) is low. Under these conditions, we produced substantial hot electron populations (diamagnetic energy > 400 J, E/sub eh/ in the range of 15 to 50 keV, and n/sub eh//n > 0.5).
Date: February 18, 1983
Creator: Stallard, B.W.
Partner: UNT Libraries Government Documents Department

Electron cyclotron heating in TMX-Upgrade

Description: TMX-Upgrade, an improved tandem mirror experiment under construction at LLNL, will use electron cyclotron resonance heating (ECRH) to create thermal barriers and to increase the center cell ion confining potential. Gyrotron oscillators (200 kW, 28 GHz) supply the heating power for the potential confined electron (fundamental heating) and the mirror-confined electrons (harmonic heating) in the thermal barriers. Important issues are temperature limitation and microstability for the hot electrons. Off-midplane heating can control anisotropy-driven microstability. Spacially restricting heating offers the possibility of temperature control by limiting the energy for resonant interaction.
Date: January 1, 1981
Creator: Stallard, B.W. & Hooper, E.B. Jr.
Partner: UNT Libraries Government Documents Department

Neutral beam current requirements for MX

Description: The neutral beam current required to sustain the MX plasma is calculated for the plasma modeled by (a) a flat-top radial density profile and (b) a diffuse radial profile. Estimates of the plasma length are obtained from Fokker-Planck calculations and a three-dimensional guiding-center equilibrium code. Beam trapping efficiency is calculated from a model taking into account the spatial dimensions of the beam and plasma. The sensitivity to variations of magnetic field and plasma beta is calculated for the plasma parameters n tau, beam current, and axial scale length.
Date: January 14, 1977
Creator: Stallard, B. W. & Rensink, M. E.
Partner: UNT Libraries Government Documents Department

Electron heat transport in improved confinement discharges in DIII-D

Description: In DIII-D tokamak plasmas with an internal transport barrier (ITB), the comparison of gyrokinetic linear stability (GKS) predictions with experiments in both low and strong negative magnetic shear plasmas provide improved understanding for ion and electron thermal transport within much of the plasma. As previously reported, the region for improved ion transport seems well characterized by the condition OE~B>Y-, where SERB is the ExB flow shear, calculated from measured quantities, and y,, is the maximum linear growth rate for ion temperature gradient (ITG) modes in the absence of flow shear. Within a limited region just inside the ITB, the electron temperature gradient (ETG) modes appear to control the electron temperature gradient and, consequently, the electron thermal transport. The increase in electron temperature gradient with more strongly negative magnetic shear is consistent with the increase in the ETG mode marginal gradient. Closer to the magnetic axis the Te profile flattens and the ETG modes are predicted to be stable. With additional core electron heating, FIR scattering measurements near the axis show the presence of high k fluctuations (12 cm-l), rotating in the electron diamagnetic drift direction. This turbulence could impact electron transport and possibly also ion transport. Thermal diffusivities for electrons, and to a lesser degree ions, increase. The ETG mode can exist at this wavenumber, but it is computed to be robustly stable near the axis.
Date: November 24, 1998
Creator: Stallard, B. W.
Partner: UNT Libraries Government Documents Department

Fokker-Planck calculations of electron cyclotron resonant heating (ECRH) in mirror geometry

Description: A time dependent, bounce-averaged Fokker-Planck code, with quasi-linear diffusion at fundamental and second harmonic frequencies, has been used to study cold plasma trapping and heating of hot electrons in mirror geometry. Both electron-electron and electron-ion Coulomb collisions are included. The code can model either cavity heating (electric field throughout cavity as in EBT) or beam controlled heating (electric field spatially restricted as in the TMX-Upgrade tandem mirror). The heating method has implications for the equilibrium energy and anisotropy of the hot electrons. In TMX-Upgrade, off-midplane heating at the second harmonic in the thermal barrier is planned as a means to control anisotropy (T/sub parallel//T/sub perpendicular/. By spatially limiting (limit in B) the microwave beam and with strong single-pass absorption, the mean hot electron energy may also be controlled since the heating rate decreases at high energy due to the relativistic mass shift of the resonance to higher magnetic field.
Date: November 25, 1981
Creator: Stallard, B.W.; Matsuda, Y. & Nevins, W.M.
Partner: UNT Libraries Government Documents Department

Coalescence of Multiple Plasmoids as a Means of Efficient Spheromak Formation

Description: We have produced single bursts of helicity from the source in the SSPX spheromak in order to study the efficiency of the simplest example of helicity injection. We find that the helicity injection rate can be written in terms of the injected current and an inductance, and that a simple circuit analogue demonstrates unambiguously the relationship of helicity to energy: helicity injection is the addition of inductive loops. While helicity balance points to the conservation of helicity, the electrical efficiency is around 15%. However, in the expulsion of the loop, electrical energy is converted to directional motion, which may be recoverable usefully as heat by collisions, thus the efficiency of the injection process is arguably quite high. Integral to this notion of helicity injection is the idea that reconnection is necessary: without disconnection from the source by a reconnection event, the spheromak fields are just proportional to the injected current. Sometimes the multiple bursts occur spontaneously and cause a step-wise increase in the field (and helicity). However, in all instances when the current remains above the ejection threshold for t &gt; 50 {micro}s, the n=l mode initiates and builds field, although with much reduced efficiency, and to a level which is symptomatic of no reconnection (B{sub spheromak} {proportional_to} I{sub inj}).
Date: February 28, 2002
Creator: Woodruff, S; McLean, H S & Stallard, B W
Partner: UNT Libraries Government Documents Department

Transport and performance in DIII-D discharges with weak or negative central magnetic shear

Description: Discharges exhibiting the highest plasma energy and fusion reactivity yet realized in the DIII-D tokamak have been produced by combining the benefits of a hollow or weakly sheared central current profile with a high confinement (H-mode) edge. In these discharges, low power neutral beam injection heats the electrons during the initial current ramp, and {open_quotes}freezes in{close_quotes} a hollow or flat central current profile. When the neutral beam power is increased, formation of a region of reduced transport and highly peaked profiles in the core often results. Shortly before these plasmas would otherwise disrupt, a transition is triggered from the low (L-mode) to high (H-mode) confinement regimes, thereby broadening the pressure profile and avoiding the disruption. These plasmas continue to evolve until the high performance phase is terminated nondisruptively at much higher {beta}{sub T} (ratio of plasma pressure to toroidal magnetic field pressure) than would be attainable with peaked profiles and an L-mode edge. Transport analysis indicates that in this phase, the ion diffusivity is equivalent to that predicted by Chang-Hinton neoclassical theory over the entire plasma volume. This result is consistent with suppression of turbulence by locally enhanced E x B flow shear, and is supported by observations of reduced fluctuations in the plasma. Calculations of performance in these discharges extrapolated to a deuterium-tritium fuel mixture indicates that such plasmas could produce a DT fusion gain Q{sub DT} = 0.32.
Date: December 1, 1996
Creator: Greenfield, C.M.; Schissel, D.P. & Stallard, B.W.
Partner: UNT Libraries Government Documents Department

Electron heat transport in improved confinement discharges in DIII-D

Description: In DIII-D tokamak plasmas with an internal transport barrier (ITB), the comparison of gyrokinetic linear stability (GKS) predictions with experiments in both low and strong negative magnetic shear plasmas provide improved understanding for electron thermal transport within the plasma. Within a limited region just inside the ITB, the electron temperature gradient (ETG) modes appear to control the electron temperature gradient and, consequently, the electron thermal transport. The increase in the electron temperature gradient with more strongly negative magnetic shear is consistent with the increase in the ETG mode marginal gradient. Closer to the magnetic axis the T{sub e} profile flattens and the ETG modes are predicted to be stable. With additional core electron heating, FIR scattering measurements near the axis show the presence of high k fluctuations (12 cm{sup {minus}1}), rotating in the electron diamagnetic drift direction. This turbulence could impact electron transport and possibly also ion transport. Thermal diffusivities for electrons, and to a lesser degree ions, increase. The ETG mode can exist at this wavenumber, but it is computed to be robustly stable near the axis. Consequently, in the plasmas the authors have examined, calculations of drift wave linear stability do not explain the observed transport near the axis in plasmas with or without additional electron heating, and there are probably other processes controlling transport in this region.
Date: January 1, 1999
Creator: Stallard, B.W.; Greenfield, C.M. & Staebler, G.M.
Partner: UNT Libraries Government Documents Department

Transport in high performance weak and negative central shear discharges in DIII-D

Description: In recent experiments in the DIII-D tokamak, the previously reported enhanced performance regime with negative central magnetic shear (NCS) has been extended to further improve fusion performance. This was done by using controlled L-H transitions to further broaden the pressure profile, thereby delaying the onset of MHD activity which would lead to the termination of the high performance phase. Such discharges have achieved record parameters for DIII-D, including D-D fusion power up to 28 kW and stored energy in excess of 4 MJ.
Date: July 1, 1996
Creator: Greenfield, C.M.; Schissel, D.P. & Stallard, B.W.
Partner: UNT Libraries Government Documents Department

Fundamental mode rectangular waveguide system for electron-cyclotron resonant heating (ECRH) for tandem mirror experiment-upgrade (TMX-U)

Description: We present a brief history of TMX-U's electron cyclotron resonant heating (ECRH) progress. We emphasize the 2-year performance of the system, which is composed of four 200-kW pulsed gyrotrons operated at 28 GHz. This system uses WR42 waveguide inside the vacuum vessel, and includes barrier windows, twists, elbows, and antennas, as well as custom-formed waveguides. Outside the TMX-U vessel are directional couplers, detectors, elbows, and waveguide bends in WR42 rectangular waveguide. An arc detector, mode filter, eight-arm mode converter, and water load in the 2.5-in. circular waveguide are attached directly to the gyrotron. Other specific areas discussed include the operational performance of the TMX-U pulsed gyrotrons, windows and component arcing, alignment, mode generation, and extreme temperature variations. Solutions for a number of these problems are described.
Date: December 1, 1983
Creator: Rubert, R.R.; Felker, B.; Stallard, B.W. & Williams, C.W.
Partner: UNT Libraries Government Documents Department

Electron cyclotron resonance heating (ECRH) in the TMX-Upgrade tandem-mirror experiment

Description: Results are described of engineering tests of operation of two gyrotrons from one power supply, tests of waveguide components and antennae, antenna design, and the x-ray shielding concept. Finally, we describe considerations of interaction with other system components.
Date: October 1, 1981
Creator: Griffin, D.H.; Rubert, R.R.; Simonen, T.C.; Stallard, B.W. & Wieskamp, T.F.
Partner: UNT Libraries Government Documents Department

Microwave measurement test results of circular waveguide components for electron cyclotron resonant heating (ECRH) of the Tandem Mirror Experiment-Upgrade (TMX-U)

Description: Development of high-power components for electron cyclotron resonant heating (ECRH) applications requires extensive testing. In this paper we describe the high-power testing of various circular waveguide components designed for application on the Tandem Mirror Experiment-Upgrade (TMX-U). These include a 2.5-in. vacuum valve, polarizing reflectors, directional couplers, mode converters, and flexible waveguides. All of these components were tested to 200 kW power level with 40-ms pulses. Cold tests were used to determine field distribution. The techniques used in these tests are illustrated. The new high-power test facility at Lawrence Livermore National Laboratory (LLNL) is described and test procedures are discussed. We discuss the following test results: efficiency at high power of mode converters, comparison of high power vs low power for waveguide components, and full power tests of the waveguide system. We also explain the reasons behind selection of these systems for use on TMX-U.
Date: December 1, 1983
Creator: Williams, C.W.; Rubert, R.R.; Coffield, F.E.; Felker, B.; Stallard, B.W. & Taska, J.
Partner: UNT Libraries Government Documents Department

Milestone report: Status report on high {beta}p experiments at high plasma current

Description: This report summarizes LLNL`s involvement in recent high {beta}{sub p} experiments on the DIII-D tokamak at General Atomics. These experiments were done in collaboration with several members of the DIII-D physics staff from GA and from other collaborating institutions and could not have succeeded without this joint effort. In this report, the authors summary a specific, limited set of experiments to extend high {beta}{sub p} operation with enhanced core confinement to higher plasma currents. The interest in these experiments stems from the non-inductive current drive requirement for steady-state advanced tokamak regimes which can most reasonably be met by operation with a high bootstrap current fraction.
Date: July 1, 1995
Creator: Casper, T.A.; James, R.A.; Rice, B.W. & Stallard, B.W.
Partner: UNT Libraries Government Documents Department

Simulations of SSPX Sustainment -- Toward a Standard Model for Spheromaks

Description: SPHERE simulations calibrated to CTX are shown to predict the correct temperature (0.12 KeV) for SSPX sustainment Shot 4624. Agreement with the temperature suggests that the Rechester-Rosenbluth thermal diffusivity included in the SPHERE heat transport equation is essentially correct. Substituting parallel heat loss as suggested by NIMROD calculations gives a temperature four times too low, while omitting Rechester-Rosenbluth transport but retaining ion classical transport gives a temperature that is 50% too high. Less certain is the magnetic buildup equation in SPHERE representing the spheromak load as a resistance adjusted to give the correct magnetic field--as is essential to obtain the correct temperature by ohmic heating. While extrapolation for long pulses using the Shot 4624 resistance does give higher magnetic field and higher temperature, the actual resistance during sustainment is still highly uncertain. In Section 6, we present a new resistance model in rough agreement with Shot 4624, but much work remains to be done. Understanding the spheromak resistance during sustainment is the main theoretical challenge for the model.
Date: January 12, 2001
Creator: Fowler, T K; Hua, D D & Stallard, B W
Partner: UNT Libraries Government Documents Department

Formation and control of plasma potentials in TMX upgrade

Description: The methods to be employed to form and control plasma potentials in the TMX Upgrade tandem mirror with thermal barriers are described. ECRH-generated mirror -confined electron plasmas are used to establish a negative potential region to isolate the end-plug and central-cell celectrons. This thermal isolation will allow a higher end-plug electron temperature and an increased central-cell confining potential. Improved axial central-cell ion confinement results since higher temperature central-cell ions can be confined. This paper describes: (1) calculations of the sensitivity of barrier formation to vacuum conditions and to the presence of impurities in the neutral beams, (2) calculations of microwave penetration and absorption used to design the ECRH system, and (3) techniques to limit electron runaway to high energies by localized microwave beams and by relativistic detuning.
Date: May 6, 1981
Creator: Simonen, T.C.; Orzechowski, T.J.; Porkolab, M. & Stallard, B.W.
Partner: UNT Libraries Government Documents Department

Dispersion relations for a plasma-filled helix-loaded-waveguide

Description: The propagation of waves on bounded, magnetized plasma columns arises in connection with a variety of applications. To this end dispersion relations axe developed for a variety of multi-region circularly symmetric configurations. These include, a sheath helix in free space, a plasma column in free space, a plasma filled conducting tube, a plasma filled sheath-helix in free space, a sheath helix within a conducting cylinder, a plasma filled sheath-helix within a conducting cylinder, and a plasma column within a sheath-helix contained within a conducting cylinder. The latter configuration is of the most interest for whistler wave excitation for plasma thruster applications, since it includes the effect of a vacuum region separating the plasma column from the helical excitation structure.
Date: January 1, 1994
Creator: Makowski, M. A.; Hooper, E. B. & Stallard, B. W.
Partner: UNT Libraries Government Documents Department

q Profile evolution and enhanced core confinement of high {beta}{sub p} plasmas in DIII-D

Description: In DIII-D the authors have investigated the long pulse evolution of high poloidal beta ({sub beta}{sub p}), double-null diverted H-mode discharges, which exhibit high bootstrap current fractions attractive for a reactor. At low currents I{sub p}, the current profile evolved over several seconds and the on-axis safety factor (q{sub 0}) increased. When q{sub 0} increased above {approximately}2, the MHD character changed from an m/n = 2/1 to an m/n = 3/1 internal kink mode, where m(n) are poloidal (toroidal) mode numbers, which then disappeared with further increases in q{sub 0}. Coincident with a strong reduction of fluctuations, the authors observed enhanced core confinement, leading to strong density peaking, a further rise in {beta}{sub p}, and a bootstrap current increasing to I{sub boot}/I{sub p} {approx} 0.8, peaked within the core. Ideal MHD calculations showed access to second stability during the density rise. During the enhanced performance phase core particle lifetime ({tau}{sub p}) and global energy lifetime ({tau}{sub E}) increased by factors of 2 and 1.2 respectively. Transport analysis showed that core particle and thermal diffusivities D{sub e} and {chi}{sub eff} approached neoclassical values. During the low current experiments, large losses of fast ions (typically {approximately}50% at 0.4 MA) were observed; at higher currents these losses are much smaller. The authors have also investigated discharges with current rampdown to high {beta}{sub p}. For a 5 to 6 {tau}{sub E} duration following rampdown, enhanced values of {beta}{sub p}, normalized toroidal beta ({beta}{sub N}), and {tau}{sub E} were obtained at high internal inductance ({ell}{sub i}). During both the ramp and the high confinement phases, fast ion losses were low ({approximately}10%). The loss then increased, correlated with an increase in the anisotropy ratio of perpendicular and parallel plasma pressure that suggests a fast ion loss mechanism coupled to the fast ion parallel energy.
Date: October 1, 1994
Creator: Stallard, B. W.; Casper, T. A. & Fenstermacher, M. E.
Partner: UNT Libraries Government Documents Department

Spheromak Impedance and Current Amplification

Description: It is shown that high current amplification can be achieved only by injecting helicity on the timescale for reconnection, {tau}{sub REC}, which determines the effective impedance of the spheromak. An approximate equation for current amplification is: dI{sub TOR}{sup 2}/dt {approx} I{sup 2}/{tau}{sub REC} - I{sub TOR}{sup 2}/{tau}{sub closed} where I is the gun current, I{sub TOR} is the spheromak toroidal current and {tau}{sub CLOSED} is the ohmic decay time of the spheromak. Achieving high current amplification, I{sub TOR} &gt;&gt; I, requires {tau}{sub REC} &lt;&lt;{tau}{sub CLOSED}. For resistive reconnection, this requires reconnection in a cold zone feeding helicity into a hot zone. Here we propose an impedance model based on these ideas in a form that can be implemented in the Corsica-based helicity transport code. The most important feature of the model is the possibility that {tau}{sub REC} actually increases as the spheromak temperature increases, perhaps accounting for the ''voltage sag'' observed in some experiments, and a tendency toward a constant ratio of field to current, B {proportional_to} I, or I{sub TOR} {approx} I. Program implications are discussed.
Date: January 31, 2002
Creator: Fowler, T K; Hua, D D & Stallard, B W
Partner: UNT Libraries Government Documents Department

Processes the Govern Helicity Injection in the SSPX Spheromak

Description: The physical processes that govern the gun-voltage and give rise to field generation by helicity injection are surveyed in the Sustained Spheromak Physics experiment (SSPX) using internal magnetic field probes and particular attention to the gun-voltage. SSPX is a gun-driven spheromak, similar in many respects to CTX, although differing substantially by virtue of a programmable vacuum field configuration. Device parameters are: diameter = 1m, I{sub tor}-400kA, T{sub e}{approx}120eV, t{sub pulse}{approx}3ms. SSPX is now in its third year of operation and has demonstrated reasonable confinement (core {chi}{sub e}{approx}30m{sup 2}/s), and evidence for a beta limit (&lt;{beta}{sub e}&gt;{sub vol}{approx}4%), suggesting that the route to high temperature is to increase the spheromak field-strength (or current amplification, A{sub I} = I{sub torr}/I{sub inj}). Some progress has been made to increase A{sub I} in SSPX (A{sub I} = 2.2), although the highest A{sub I} observed in a spheromak of 3 has yet to be beaten. We briefly review helicity injection as the paradigm for spheromak field generation. SSPX results show that the processes that give efficient injection of helicity are inductive, and that these processes rapidly terminate when the current path ceases to change. The inductive processes are subsequently replaced by ones that resistively dissipate the injected helicity. This result means that efficient helicity injection can be achieved by harnessing the inductive processes, possibly by pulsing the gun. A pulsed build-up scenario is presented which gives A{sub I} &gt; 3 and emphasizes the need to maintain reasonable confinement while the field of the spheromak is being built.
Date: October 8, 2002
Creator: Woodruff, S; Stallard, B W; Holcomb, C T & Cothran, C
Partner: UNT Libraries Government Documents Department

Focusing twist reflector for electron-cyclotron resonance heating in the Tandem Mirror Experiment-Upgrade

Description: A twist reflector plate is described that linearly polarizes and focuses the TE/sub O/sub 1// circular waveguide mode for heating hot electrons in the thermal barrier of the Tandem Mirror Experiment-Upgrade (TMX-U). The plate polarizing efficiency is 95%, and it has operated satisfactorily at 150 kW power level.
Date: May 1, 1984
Creator: Stallard, B.W.; Coffield, F.E.; Felker, B.; Taska, J.; Christensen, T.E.; Gallagher, N.C. Jr. et al.
Partner: UNT Libraries Government Documents Department

Engineering design of the interaction waveguide for high-power accelerator-driven microwave free-electron lasers

Description: Linear induction accelerators (LIAs) operating at beam energies of a few million electron volts and currents of a few thousand amperes are suitable drivers for free-electron lasers (FELs). Such lasers are capable of producing gigawatts of peak power and megawatts of average power at microwave frequencies. Such devices are being studied as possible power sources for future high-gradient accelerators and are being constructed for plasma heating applications. At high power levels, the engineering design of the interaction waveguide presents a challenge. This paper discusses several concerns, including electrical breakdown and metal fatigue limits, choice of material, and choice of operating propagation mode. 13 refs., 3 figs.
Date: March 16, 1989
Creator: Hopkins, D.B.; Clay, H.W.; Stallard, B.W.; Throop, A.L.; Listvinsky, G. & Makowski, M.A.
Partner: UNT Libraries Government Documents Department