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Optimized profiles for improved confinement and stability in the DIII-D tokamak

Description: Simultaneous achievement of high energy confinement, {tau}{sub E}, and high plasma beta, {beta}, leads to an economically attractive compact tokamak fusion reactor. High confinement enhancement, H = {tau}{sub E}/{tau}{sub E-ITER89P} = 4, and high normalized beta {beta}{sub N} = {beta}/(I/aB) = 6%-m-T/MA, have been obtained in DIII-D experimental discharges. These improved confinement and/or improved stability limits are observed in several DIII-D high performance operational regimes: VH-mode, high {ell}{sub i} H-mode, second stable core, and high beta poloidal. The authors have identified several important features of the improved performance in these discharges: details of the plasma shape, toroidal rotation or ExB flow profile, q profile and current density profile, and pressure profile. From the improved physics understanding of these enhanced performance regimes, they have developed operational scenarios which maintain the essential features of the improved confinement and which increase the stability limits using localized current profile control. The stability limit is increased by modifying the interior safety factor profile to be nonmonotonic with high central q, while maintaining the edge current density consistent with the improved transport regimes and the high edge bootstrap current. They have calculated high beta equilibria with {beta}{sub N} = 6.5, stable to ideal n = 1 kinks and stable to ideal ballooning modes. The safety factor at the 95% flux surface is 6, the central q value is 3.9 and the minimum in q is 2.6. The current density profile is maintained by the natural profile of the bootstrap current, and a modest amount of electron cyclotron current drive.
Date: February 1, 1995
Creator: Taylor, T.S.; St. John, H. & Turnbull, A.D.
Partner: UNT Libraries Government Documents Department

Stabilization of the external kink and control of the resistive wall mode in tokamaks

Description: One promising approach to maintaining stability of high beta tokamak plasmas is the use of a conducting wall near the plasma to stabilize low-n ideal MHD instabilities. However, with a resistive wall, either plasma rotation or active feedback control is required to stabilize the more slowly growing resistive wall modes (RWMs). Experiments in the DIII-D, PBHX-M, and HBT-EP tokamaks have demonstrated that plasmas with a nearby conducting wall can remain stable to the n = 1 ideal external kink above the beta limit predicted with the wall at infinity, with durations in DIII-D up to 30 times {tau}{sub w}, the resistive wall time constant. More recently, detailed, reproducible observation of the n = 1 RWM has been possible in DIII-D plasmas above the no-wall beta limit. The DIII-D measurements confirm characteristics common to several RWM theories. The mode is destabilized as the plasma rotation at the q = 3 surface decreases below a critical frequency of 1 to 7 kHz. The measured mode growth times of 2 to 8 ms agree with measurements and numerical calculations of the dominant DIII-D vessel eigenmode time constants, {tau}{sub w}. From its onset, the RWM has little or no toroidal rotation and rapidly reduces the plasma rotation to zero. Both DIII-D and HBT-EP have adopted the smart shell concept as an initial approach to control of these slowly growing RWMs; external coils are controlled by a feedback loop designed to make the resistive wall appear perfectly conducting by maintaining a net zero radial field at the wall. Initial experiment results from DIII-D have yielded encouraging results.
Date: January 1999
Creator: Garofalo, A. M.; Turnbull, A. D. & Strait, E. J.
Partner: UNT Libraries Government Documents Department

Wall stabilization of rotating high {beta} discharges in DIII-D

Description: Wall stabilization of the ideal n = 1 external kink mode is shown to be possible in high {beta}, rotating DII-D plasmas for times much longer than the resistive wall penetration time. The gain in {ss} can be more than 30% above the calculated stability limit with no wall stabilization. Stabilization from the resistive wall is found to require plasma rotation speeds of several kHz; otherwise, unstable locked or slowly rotating modes appear, with growth times of the order of the wall penetration time, which ultimately lead to termination of the discharge. The slowly rotating modes have the characteristics expected of the theoretically predicted resistive wall mode in an ideal plasma.
Date: October 1, 1994
Creator: Turnbull, A.D.; Taylor, T.S. & Strait, E.J.
Partner: UNT Libraries Government Documents Department

Current drive and profile control in low aspect ratio tokamaks

Description: The key to the theoretically predicted high performance of a low aspect ratio tokamak (LAT) is its ability to operate at very large plasma current*I{sub p}. The plasma current at low aspect ratios follows the approximate formula: I{sub p} {approximately} (5a{sup 2}B{sub t}/Rq{psi}) [(1 + {kappa}{sup 2})/2] [A/(A {minus} 1)] where A {quadruple_bond} R/a which was derived from equilibrium studies. For constant q{psi} and B{sub t}, I{sub p} can increase by an order of magnitude over the case of tokamaks with A {approx_gt} 2.5. The large current results in a significantly enhanced {beta}{sub t} ({quadruple_bond} {beta}{sub N}I{sub p}/aB{sub t}) possibly of order unity. It also compensates for the reduction in A to maintain the same confinement performance assuming the confinement time {tau} follows the generic form {approximately} HI{sub p}P{sup {minus}1}/{sup 2}R{sup 3}/{sup 2}{kappa}{sup 1}/{sup 2}. The initiation and maintenance of such a large current is therefore a key issue for LATs.
Date: July 1, 1995
Creator: Chan, V.S.; Chiu, S.C.; Lin-Liu, Y.R.; Miller, R.L. & Turnbull, A.D.
Partner: UNT Libraries Government Documents Department

A CLASS OF HIGH EBP EQUILIBRIA IN STRONGLY FINITE ASPECT RATIO TOKAMAK PLASMAS

Description: OAK B202 A CLASS OF HIGH EBP EQUILIBRIA IN STRONGLY FINITE ASPECT RATIO TOKAMAK PLASMAS. A class of very high poloidal beta ({beta}{sub p}) equilibria is exhibited in which {var_epsilon}{beta}{sub p} ({var_epsilon} is the inverse aspect ratio) exceeds analytic equilibrium limits previously anticipated from simplified large aspect ratio models, as well as previous experimental equilibrium limits. The extension in these limits is shown to be due to a combination of finite aspect ratio effects and strong cross section shaping. In a conventional size configuration, equilibria with {var_epsilon}{beta}{sub p} = 3 exist, which is 50% higher than both the previously observed record and the analytically predicted limit. For very low aspect ratio with {var_epsilon}{sup -1} = 1.4, typical of spherical tori, values of {var_epsilon}{beta}{sub p} = 5 are possible.
Date: August 1, 2002
Creator: LIN-LIU, Y.R.; TURNBULL, A.D.; MILLER, R.L.; CHAN, V.S. & POLITZER, P.A.
Partner: UNT Libraries Government Documents Department

Stable bootstrap-current driven equilibria for low aspect ratio tokamaks

Description: Low aspect ratio tokamaks can potentially provide a high ratio of plasma pressure to magnetic pressure {beta} and high plasma current I at a modest size, ultimately leading to a high power density compact fusion power plant. For the concept to be economically feasible, bootstrap current must be a major component of the plasma current. A high value of the Troyon factor {beta}{sub N} and strong shaping are required to allow simultaneous operation at high {beta} and high bootstrap current fraction. Ideal magnetohydrodynamic stability of a range of equilibria at aspect ratio 1.4 is systematically explored by varying the pressure profile and shape. The pressure and current profiles are constrained in such a way as to assure complete bootstrap current alignment. Both {beta}{sub N} and {beta} are defined in terms of the vacuum toroidal field. Equilibria with {beta}{sub N} {ge} 8 and {beta} - 35% to 55% exist which are stable to n = {infinity} ballooning modes, and stable to n = 0, 1,2,3 kink modes with a conducting wall. The dependence of {beta} and {beta}{sub N} with respect to aspect ratio is also considered.
Date: August 1, 1996
Creator: Miller, R.L.; Lin-Liu, Y.R.; Turnbull, A.D.; Chan, V.S.; Pearlstein, L.D.; Sauter, O. et al.
Partner: UNT Libraries Government Documents Department

Observation and Analysis of Resistive Instabilities in Negative Central Shear in DIII-D Discharges with L-Mode Edge

Description: In DIII-D plasmas with L-mode edge and negative central shear (q{sub axis}-q{sub min} {approx}0.3 to 0.5), an interchange-like instability has been observed [1]. The instability and a subsequent tearing mode cause reduction of the core electron temperature and plasma rotation, and therefore the instability affects discharge evolution and the desired high performance is not achieved. Stability analyses indicate robust ideal stability, while the Resistive Interchange Mode criterion is marginal and the instability appears to be localized initially. Based on this, we believe that the mode is, most likely, a Resistive Interchange Mode. The amplitude of the instability is correlated with the location of the q{sub min} surface and inversely with the fast-ion pressure. There is indication that the interchange-like instability may be ''seeding'' the tearing mode that sometimes follows the interchange-like instability.
Date: July 1, 2002
Creator: Jayakumar, R.J.; Austin, M.E.; Brennan, D.P.; Chu, M.S.; Luce, T.C.; Strait, E.J. et al.
Partner: UNT Libraries Government Documents Department

ARIES-ST STUDIES REPORT FOR THE PERIOD JANUARY 1, 1998 THROUGH DECEMBER 31, 1998

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

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

The Effect of Plasma Shape on H-Mode Pedestal Characteristics on DIII-D

Description: The characteristics of the H-mode are studied in discharges with varying triangularity and squareness. The pressure at the top of the H-mode pedestal increases strongly with triangularity primarily due to an increase in the margin by which the edge pressure gradient exceeds the ideal ballooning mode first stability limit. Two models are considered for how the edge may exceed the ballooning mode limit. In one model [1], access to the ballooning mode second stable regime allows the edge pressure gradient and associated bootstrap current to continue to increase until an edge localized, low toroidal mode number, ideal kink mode is destabilized. In the second model [2], the finite width of the H-mode transport barrier, and diamagnetic effects raise the pressure gradient limit above the ballooning mode limit. We observe a weak inverse dependence of the width of the H-mode transport barrier, {Delta}, on triangularity relative to the previously obtained [3] scaling {Delta} {infinity} ({beta}{sub P}{sup PED}){sup 1/2}. The energy loss for Type I ELMs increases with triangularity in proportion to the pedestal energy increase. The temperature profile is found to respond stiffly to changes in T{sup PED} at low temperature, while at high temperature the response is additive. The response of the density profile is also found to play a role in the response of the total stored energy to changes in the W{sup PED}.
Date: December 1, 1999
Creator: Osborne, T.H.; Ferron, J.R.; Groebner, R.J.; Lao, L.L.; Leonard, A.W.; Maingi, R. et al.
Partner: UNT Libraries Government Documents Department

SUSTAINED STABILIZATION OF THE RESISTIVE WALL MODE BY PLASMA ROTATION IN THE DIII-D TOKAMAK

Description: OAK-B135 A path to sustained stable operation, at plasma pressure up to twice the ideal magnetohydrodynamic (MHD) n = 1 free-boundary pressure limit, has been discovered in the DIII-D tokamak. Tuning the correction of the intrinsic magnetic field asymmetries so as to minimize plasma rotation decay during the high beta phase and increasing the angular momentum injection, have allowed maintaining the plasma rotation above that needed for stabilization of the resistive wall mode (RWM). A new method to determine the improved magnetic field correction uses feedback to sense and minimize the resonant plasma response to the non-axisymmetric field. At twice the free-boundary pressure limit, a disruption precursor is observed, which is consistent with having reached the ''ideal wall'' pressure limit predicted by stability calculations.
Date: October 1, 2001
Creator: GAROFALO,A.M; STRAIT,E.J; JOHNSON,L.C; LA HAYE,R.J; LAZARUS,E.A; NAVRATIL,G.A et al.
Partner: UNT Libraries Government Documents Department

OVERVIEW OF H-MODE PEDESTAL RESEARCH ON DIII-D

Description: Developing an understanding of the processes that control the H-mode transport barrier is motivated by the significant impact this small region (typically <2% of the minor radius) can have on overall plasma performance. Conditions at the inner edge of the H-mode transport barrier can strongly influence the overall energy confinement, and the maximum density, and therefore fusion power, that can be achieved with the typically flat H-mode density profiles [1,2]. The ELM instability, which usually regulates the pressure gradient in the H-mode edge, can result in large power loads to, and erosion of, the divertor targets in a reactor scale device [3]. The goal of H-mode pedestal research at DIII-D is to: (1) develop a physics based model that would allow prediction of the conditions at the top of the H-mode pedestal, (2) develop an understanding of processes which control Type I ELM effects in the core and divertor, and (3) explore alternatives to the Type I ELM regime.
Date: July 1, 2001
Creator: OSBORNE, T.H.; BURRELL, K.H.; CARLSTROM, T.N.; CHU, M.S.; DOYLE, E.J.; FERRON, J.R. et al.
Partner: UNT Libraries Government Documents Department

Physics Basis for the Advanced Tokamak Fusion Power Plant ARIES-AT

Description: The advanced tokamak is considered as the basis for a fusion power plant. The ARIES-AT design has an aspect ratio of A always equal to R/a = 4.0, an elongation and triangularity of kappa = 2.20, delta = 0.90 (evaluated at the separatrix surface), a toroidal beta of beta = 9.1% (normalized to the vacuum toroidal field at the plasma center), which corresponds to a normalized beta of bN * 100 x b/(I(sub)P(MA)/a(m)B(T)) = 5.4. These beta values are chosen to be 10% below the ideal-MHD stability limit. The bootstrap-current fraction is fBS * I(sub)BS/I(sub)P = 0.91. This leads to a design with total plasma current I(sub)P = 12.8 MA, and toroidal field of 11.1 T (at the coil edge) and 5.8 T (at the plasma center). The major and minor radii are 5.2 and 1.3 m, respectively. The effects of H-mode edge gradients and the stability of this configuration to non-ideal modes is analyzed. The current-drive system consists of ICRF/FW for on-axis current drive and a lower-hybrid system for off-axis. Tran sport projections are presented using the drift-wave based GLF23 model. The approach to power and particle exhaust using both plasma core and scrape-off-layer radiation is presented.
Date: October 7, 2003
Creator: Jardin, S.C.; Kessel, C.E.; Mau, T.K.; Miller, R.L.; Najmabadi, F.; Chan, V.S. et al.
Partner: UNT Libraries Government Documents Department

Optimization of negative central shear discharges in shaped cross sections

Description: Magnetohydrodynamic (MHD) stability analyses of Negative Central Shear (NCS) equilibria have revealed a new understanding of the limiting MHD instabilities in NCS experiments. Ideal stability calculations show a synergistic effect between cross section shape and pressure profile optimization; strong shaping and broader pressure independently lead to moderately higher {Beta} limits, but broadening of the pressure profile in a strongly dee-shaped cross- section leads to a dramatic increase in the ideal {Beta} limit. Localized resistive interchange (RI) modes can be unstable in the negative shear region and are most restrictive for peaked pressure profiles. Resistive global modes can also be destabilized significantly below the ideal P limit. Experiments largely confirm the general trends, and diagnostic measurements and numerical stability calculations are found to be in good qualitative agreement. Observed disruptions in NCS discharges with L-mode edge and strongly peaked pressure, appear to be initiated by interactions between the RI, and the global ideal and resistive modes.
Date: October 1, 1996
Creator: Turnbull, A.D., Chu, M.S., Taylor, T.S., Casper, T.A., Rice, B.W.; Greene, J.M., Greenfield, C.M., La Haye, R.J., Lao, L.L., Lee, B.J.; Miller, R.L., Ren, C., Strait, E.J., Tritz, K.; Rettig, C.L., Rhodes, T.L. & Sauter, O.
Partner: UNT Libraries Government Documents Department

Characterization and Modification of Edge-Driven Instabilities in the DIII-D Tokamak

Description: The character of edge localized modes (ELMs) and the height of the edge pressure pedestal in DIII-D tokamak H-mode discharges have been modified by varying the discharge shape (triangularity and squareness) and the safety factor, increasing the edge radiation, and injecting deuterium pellets. Changes in the ELM frequency and amplitude, and the magnitude of the edge pressure gradient, and changes in the calculated extent of the region of access to the ballooning mode second stability regime are observed.
Date: July 1, 1999
Creator: Ferron, J.R.; Lao, L.L.; Osborne, T.H.; Strait, E.J.; Turnbull, A.D.; Miller, R.L. et al.
Partner: UNT Libraries Government Documents Department

Advanced Tokamak Scenario Modeling with Off-Axix ECH in DIII-D

Description: Time-dependent simulations with transport coefficients derived from experimentally achieved discharges are used to explore the capability of off-axis electron cyclotron current drive (ECCD) to control hollow current profiles in negative central shear discharges. Assuming these transport coefficients remain unchanged at higher EC power levels, the simulation results show that high confinement, high normalized beta and high bootstrap fraction can be achieved with EC power expected to be available in the near future in the DIII-D tokamak.
Date: July 1, 1999
Creator: Murakami, M.; Casper, T.A.; Lao, L.L.; St. John, H.E.; Deboo, J.C.; Greenfield, C.M. et al.
Partner: UNT Libraries Government Documents Department

ACTIVE FEEDBACK STABILZATION OF THE RESISTIVE WALL MODE ON THE DIII-D DEVICE

Description: A proof of principle magnetic feedback stabilization experiment has been carried out to suppress the resistive wall mode (RWM), a branch of the ideal magnetohydrodynamic (MHD) kink mode under the influence of a stabilizing resistive wall, on the DIII-D tokamak device [Plasma Phys. and Contr. Fusion Research (International Atomic Energy Agency, Vienna, 1986), p. 159]. The RWM was successfully suppressed and the high beta duration above the no wall limit was extended to more than 50 times the resistive wall flux diffusion time. It was observed that the mode structure was well preserved during the time of the feedback application. Several lumped parameter formulations were used to study the feedback process. The observed feedback characteristics are in good qualitative agreement with the analysis. These results provide encouragement to future efforts towards optimizing the RWM feedback methodology in parallel to what has been successfully developed for the n = 0 vertical positional control. Newly developed MHD codes have been extremely useful in guiding the experiments and in providing possible paths for the next step.
Date: November 1, 2000
Creator: OKABAYASHI, M.; BIALEK, J.; CHANCE, M.S.; CHU, M.S.; FREDRICKSON, E.D.; GAROFALO, A.M. et al.
Partner: UNT Libraries Government Documents Department

PROGRESS TOWARD SUSTAINED HIGH-PERFORMANCE ADVANCED TOKAMAK DISCHARGES IN DIII-D

Description: Key elements of a sustained advanced tokamak discharge in DIII-D are a large fraction of the total current from bootstrap current (f{sub BS}) and parameters that optimize the capability to use electron cyclotron current drive (ECCD) at {rho} {approx} 0.5 to maintain the desired current profile [1-4]. Increased f{sub BS} results from increasing both the normalized beta ({beta}{sub N}) and the minimum value of the safety factor (q{sub min}). Off-axis ECCD is, for the available gyrotron power, optimized at high {beta}{sub N}, high electron temperature (T{sub e}) and low electron density (n{sub e}). As previously reported [2-4], these required elements have been separately demonstrated: density control at high {beta}{sub N} with n{sub e} {le} 5 x 10{sup 19} m{sup -3} using divertor-region pumping, stability at high {beta}, and off-axis ECCD at the theoretically predicted efficiency. This report summarizes recent work on optimizing and integrating these results through evaluation of the dependence of the beta limit on q{sub min} and q{sub 95}, exploration of discharges with relatively high q{sub min}, testing of feedback control of T{sub e} for control of the q profile evolution, and modification of the current profile time evolution when ECCD is applied.
Date: July 1, 2002
Creator: FERRON, J.R.; BREEAN, D.P.; CASPER, T.A.; GAROFALO, A.M.; GREENFIELD, C.M.; HYATT, A.W. et al.
Partner: UNT Libraries Government Documents Department

LONG-PULSE, HIGH-PERFORMANCE DISCHARGES IN THE DIII-D TOKAMAK

Description: Significant progress in obtaining high performance discharges for many energy confinement times in the DIII-D tokamak has been realized since the previous IAEA meeting. In relation to previous discharges, normalized performance {approx}10 has been sustained for >5 {tau}{sub E} with q{sub min} >1.5. (The normalized performance is measured by the product {beta}{sub N} H{sub 89} indicating the proximity to the conventional {beta} limits and energy confinement quality, respectively.) These H-mode discharges have an ELMing edge and {beta} {approx}{le} 5%. The limit to increasing {beta} is a resistive wall mode, rather than the tearing modes previously observed. Confinement remains good despite the increase in q. The global parameters were chosen to optimize the potential for fully non-inductive current sustainment at high performance, which is a key program goal for the DIII-D facility in the next two years. Measurement of the current density and loop voltage profiles indicate {approx}75% of the current in the present discharges is sustained non-inductively. The remaining ohmic current is localized near the half radius. The electron cyclotron heating system is being upgraded to replace this remaining current with ECCD. Density and {beta} control, which are essential for operating advanced tokamak discharges, were demonstrated in ELMing H-mode discharges with {beta}{sub N}H{sub 89} {approx} 7 for up to 6.3 s or {approx} 34 {tau}{sub E}. These discharges appear to be in resistive equilibrium with q{sub min} {approx} 1.05, in agreement with the current profile relaxation time of 1.8 s.
Date: October 1, 2000
Creator: LUCE, T.C.; WADE, M.R.; POLITZER, P.A.; ALLEN, S.L.; AUSTIN, M E.; BAKER, D.R. et al.
Partner: UNT Libraries Government Documents Department