E. D. Fredrickson

Simulations of deuterium-tritium experiments in TFTR

A transport code (TRANSP) is used to simulate future deuterium-tritium (DT) experiments in TFTR. The simulations are derived from 14 TFTR DD discharges, and the modelling of one supershot is discussed in detail to indicate the degree of accuracy of the TRANSP modelling. Fusion energy yields and alpha particle parameters are calculated, including profiles of the alpha slowing down time, the alpha average energy, and the Alfven speed and frequency. Two types of simulation are discussed. The main emphasis is on the DT equivalent, where an equal mix of D and T is substituted for the D in the initial target plasma, and for the D0 in the neutral beam injection, but the other measured beam and plasma parameters are unchanged. This simulation does not assume that alpha heating will enhance the plasma parameters or that confinement will increase with the addition of tritium. The maximum relative fusion yield calculated for these simulations is QDT ~ 0.3, and the maximum alpha contribution to the central toroidal β is βα(0) ~ 0.5%. The stability of toroidicity induced Alfven eigenmodes (TAE) and kinetic ballooning modes (KBM) is discussed. The TAE mode is predicted to become unstable for some of the simulations, particularly after the termination of neutral beam injection. In the second type of simulation, empirical supershot scaling relations are used to project the performance at the maximum expected beam power. The MHD stability of the simulations is discussed

Active feedback stabilization of the resistive wall mode on the DIII-D device

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.

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

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 magnetohydrodynamic 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). Previous experiments 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. Recently, extension of the wall stabilized lifetime τL to more than 30 times the resistive wall time constant τw and detailed, reproducible observation of the n=1 RWM have been possible in DIII-D [Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1986), p. 159] 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 surfac...

High poloidal beta equilibria in the Tokamak Fusion Test Reactor limited by a natural inboard poloidal field null

Recent operation of the Tokamak Fusion Test Reactor (TFTR) [Plasma Phys. Controlled Nucl. Fusion Research 1, 51 (1986)] has produced plasma equilibria with values of Λ≡βp eq+li/2 as large as 7, eβp dia≡2μ0e〈p⊥〉/〈〈Bp〉〉2 as large as 1.6, and Troyon normalized diamagnetic beta [Plasma Phys. Controlled Fusion 26, 209 (1984); Phys. Lett. 110A, 29 (1985)], βNdia≡108〈βt⊥〉aB0/Ip as large as 4.7. When eβp dia≳1.25, a separatrix entered the vacuum chamber, producing a naturally diverted discharge that was sustained for many energy confinement times, τE. The largest values of eβp and plasma stored energy were obtained when the plasma current was ramped down prior to neutral beam injection. The measured peak ion and electron temperatures were as large as 24 and 8.5 keV, respectively. Plasma stored energy in excess of 2.5 MJ and τE greater than 130 msec were obtained. Confinement times of greater than 3 times that expected from L‐mode predictions have been achieved. The fusion power gain QDD reached a value of 1.3×10−...

Tomography of full sawtooth crashes on the Tokamak Fusion Test Reactor

Full sawtooth crashes in high temperature plasmas have been investigated on the Tokamak Fusion Test Reactor (TFTR) [Plasma Phys. Controlled Fusion 33, 1509 (1991)]. A strong asymmetry in the direction of major radius, a feature of the ballooning mode, and a remaining m=1 region after the crash have been observed with electron cyclotron emission image reconstructions. The TFTR data is not consistent with two‐dimensional (2‐D) models; it rather suggests a three‐dimensional (3‐D) localized reconnection arising on the bad curvature side. This process explains the phenomenon of fast heat transfer which keeps the condition q0<1.

Plasma-material interactions in TFTR

This paper presents a summary of plasma-material interactions which influence the operation of TFTR with high current (≤ 2.2 MA) ohmically heated, and high-power (∼ 10 MW) neutral-beam heated plasmas. The conditioning procedures which are applied routinely to the first-wall hardware are reviewed. Fueling characteristics during gas, pellet, and neutral-beam fueling are described. Recycling coefficients near unity are observed for most gas fueled discharges. Gas fueled discharges after helium discharge conditioning of the toroidal bumper limiter, and discharges fueled by neutral beams and pellets, show R<1. In the vicinity of the gas fueled density limit (at ne = 5–6 × 1019 m−3) values of Zeff are ≦1.5. Increases in Zeff of ≦1 have been observed with neutral beam heating of 10 MW. The primary low Z impurity is carbon with concentrations decreasing from ∼10% to <1% with increasing ne. Oxygen densities tend to increase with ne, and at the ohmic plasma density limit oxygen and carbon concentrations are comparable. Chromium getter experiments and He2+/D+ plasma comparisons indicate that the limiter is the primary source of carbon and that the vessel wall is a significant source of the oxygen impurity. Metallic impurities, consisting of the vacuum vessel metals (Ni, Fe, Cr) have significant (∼10−4 ne) concentrations only at low plasma densities (ne <1019 m−3). The primary source of metallic impurities is most likely ion sputtering from metals deposited on the carbon limiter surface.

Beta-induced Alfvén-acoustic eigenmodes in National Spherical Torus Experiment and DIII-D driven by beam ions

Kinetic theory and experimental observations of a special class of energetic particle driven instabilities called here beta-induced Alfven-acoustic eigenmodes (BAAEs) are reported confirming, previous results [N. N. Gorelenkov et al., Plasma Phys. Controlled Fusion 49, B371 (2007)]. The kinetic theory is based on the ballooning dispersion relation where the drift frequency effects are retained. BAAE gaps are recovered in kinetic theory. It is shown that the observed certain low-frequency instabilities on DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] and National Spherical Torus Experiment [M. Ono, S. M. Kaye, Y.-K. M. Peng et al., Nucl. Fusion 40, 557 (2000)] are consistent with their identification as BAAEs. BAAEs deteriorate the fast ion confinement in DIII-D and can have a similar effect in next-step fusion plasmas, especially if excited together with multiple global toroidicity-induced shear Alfven eigenmode instabilities. BAAEs can also be used to diagnose safety factor profiles, a technique know...

Correlations of heat and momentum transport in the TFTR tokamak

Measurements of the toroidal rotation speed vφ(r) driven by neutral beam injection in tokamak plasmas and, in particular, simultaneous profile measurements of vφ, Ti, Te, and ne, have provided new insights into the nature of anomalous transport in tokamaks. Low‐recycling plasmas heated with unidirectional neutral beam injection exhibit a strong correlation among the local diffusivities, χφ≊χi>χe. Recent measurements have confirmed similar behavior in broad‐density L‐mode plasmas. These results are consistent with the conjecture that electrostatic turbulence is the dominant transport mechanism in the tokamak fusion test reactor tokamak (TFTR) [Phys. Rev. Lett. 58, 1004 (1987)], and are inconsistent with predictions both from test‐particle models of strong magnetic turbulence and from ripple transport. Toroidal rotation speed measurements in peaked‐density TFTR ‘‘supershots’’ with partially unbalanced beam injection indicate that momentum transport decreases as the density profile becomes more peaked. In hi...

A description of the full-particle-orbit-following SPIRAL code for simulating fast-ion experiments in tokamaks

The numerical methods used in the full particle-orbit following SPIRAL code are described and a number of physics studies performed with the code are presented to illustrate its capabilities. The SPIRAL code is a test-particle code and is a powerful numerical tool to interpret and plan fast-ion experiments in tokamaks. Gyro-orbit effects are important for fast ions in low-field machines such as NSTX and to a lesser extent in DIII-D. A number of physics studies are interlaced between the description of the code to illustrate its capabilities. Results on heat loads generated by a localized error-field on the DIII-D wall are compared with measurements. The enhanced Triton losses caused by the same localized error-field are calculated and compared with measured neutron signals. Magnetohydrodynamic (MHD) activity such as tearing modes and toroidicity-induced Alfven eigenmodes (TAEs) have a profound effect on the fast-ion content of tokamak plasmas and SPIRAL can calculate the effects of MHD activity on the confined and lost fast-ion population as illustrated for a burst of TAE activity in NSTX. The interaction between ion cyclotron range of frequency (ICRF) heating and fast ions depends solely on the gyro-motion of the fast ions and is captured exactly in the SPIRAL code. A calculation of ICRF absorption on beam ions in ITER is presented. The effects of high harmonic fast wave heating on the beam-ion slowing-down distribution in NSTX is also studied.

β limit disruptions in the Tokamak Fusion Test Reactor

A disruptive β limit (β=plasma pressure/magnetic pressure) is observed in high‐performance plasmas in the Tokamak Fusion Test Reactor (TFTR) [K. M. McGuire et al., Plasma Phys. Controlled Nuclear Fusion 1, 421 (1987)]. The magnetohydrodynamic character of these disruptions differs substantially from the disruptions in high‐density plasmas (density limit disruptions) on TFTR. The high β disruptions can occur with less than a millisecond warning in the form of a fast growing precursor. The precursor appears to be an n=1 kink strongly coupled through finite β effects and toroidal terms to higher m components. It does not have the ‘‘cold bubble’’ structure found in density limit disruptions. The n=1 kink, in turn, appears to excite a ballooning‐type mode that may contribute to the thermal quench.