R. L. Miller's research while affiliated with General Atomics and other places
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Publications (87)
A new understanding of edge localized modes (ELMs) in tokamak discharges is emerging (Snyder P B et al 2002 Phys. Plasmas 9 2037), in which the ELM is an essentially ideal magnetohydrodynamic (MHD) instability and the ELM severity is determined by the radial width of the linearly unstable MHD kink modes. A detailed, comparative study of the penetra...
A class of very high poloidal beta (betap) equilibria is exhibited in which Vbetap (V 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 aspe...
The magnetic field of a low aspect ratio tokamak (LART) deviates rather significantly from the approximately 1/R dependence of conventional tokamaks. The parameterization of current drive efficiency on the basis of conventional large aspect ratio tokamaks becomes inaccurate. The physics of high harmonic ion cyclotron fast wave current drive (FWCD)...
Strong shaping, favourable for stability and improved energy confinement, together with a significant expansion of the central region of improved confinement in negative central magnetic shear target plasmas, increased the maximum fusion power produced in DIII-D by a factor of 3. Using deuterium plasmas, the highest fusion power gain, the ratio of...
OAK B202 A CLASS OF HIGH EBP EQUILIBRIA IN STRONGLY FINITE ASPECT RATIO TOKAMAK PLASMAS. A class of very high poloidal beta (β{sub p}) equilibria is exhibited in which {var_epsilon}β{sub p} ({var_epsilon} is the inverse aspect ratio) exceeds analytic equilibrium limits previously anticipated from simplified large aspect ratio models, as well as p...
Systematic stability studies of the negative central shear (NCS) configuration reveal a synergistic relationship between the gains in the ideal n = 1 magnetohydrodynamic (MHD) β limit from optimizing the profiles and from optimizing the shape. For a circular cross-section with highly peaked pressure profiles, βN = β/(I/aB) is limited to βN~2% (mT/M...
A number of edge plasma physics phenomena are considered to determine tokamak performance: transport barrier,
edge MHD instabilities and plasma flow. These phenomena are thought to be causally related: a spontaneous increase in
the plasma flow (actually, its radial variation) suppresses heat and particle fluxes at the plasma edge to form a
trans...
The frequency and amplitude of edge localized instabilities in DIII-D tokamak H mode discharges are shown to depend on the discharge shape squareness. An abrupt increase in instability frequency and decreases in instability amplitude and edge pressure gradient are observed when the squareness is changed to a sufficiently large or a sufficiently sma...
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 ≈ 2-9 and a fast growth time γ-1 = 20-150 μs are often observed prior to the first giant type I ELM in discharges with mo...
The requirements to stabilize microinstabilities with velocity shear in tokamaks are examined for both aspect ratio A = 3 and A = 1.4. A comprehensive linear gyrokinetic code is used to compute growth rates in realistic numerical equilibria. Growth rates for A = 3 and A = 1.4 are generally similar for electron drift modes and ion temperature gradie...
A new computational tool, edge localized instabilities in tokamaks equilibria (ELITE), has been developed to help our understanding of short wavelength instabilities close to the edge of tokamak plasmas. Such instabilities may be responsible for the edge localized modes observed in high confinement H-mode regimes, which are a serious concern for ne...
A modified lattice Boltzmann algorithm is shown to have much better stability to growing temperature perturbations, when compared with the standard lattice Boltzmann algorithm. The damping rates of long-wavelength waves, which determine stability, are derived using a collisional equilibrium distribution function which has the property that the Eule...
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...
The amplitude and frequency of modes driven in the edge region of tokamak high mode (H-mode) discharges [type I edge-localized modes (ELMs)] are shown to depend on the discharge shape. The measured pressure gradient threshold for instability and its scaling with discharge shape are compared with predictions from ideal magnetohydrodynamic theory for...
A generalization of the circular ŝ-α local magnetohydrodynamic (MHD) equilibrium model to finite aspect ratio (A), elongation (κ), and triangularity (δ) has been added to a gyrokinetic stability code and our gyrofluid nonlinear ballooning mode code for ion temperature gradient (ITG) turbulence. This allows systematic studies of stability and transp...
Equilibrium and stability analyses have identified a class of tokamak configurations with conventional safety factor profiles (q0 ∼ qmin≳1) at moderately high li(li ∼ 1.0), and high normalized β(βN ∼ 3.5–4.0), that are stable to the ideal n = 1 kink without the requirement of wall stabilization. In contrast to previously identified high li, high βN...
In DIII-D [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] 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. Wit...
The ideal magnetohydrodynamic (MHD) stability of the tokamak edge is analyzed, with particular emphasis on radially localized instabilities; it is proposed that these are responsible for edge pressure gradient limits and edge localized modes (ELMS). Data and stability calculations from DIII-D [to appear in Proceedings of the 16th International Conf...
Optimization of the higher order moments—specifically the squareness—of a tokamak cross-section can significantly enhance the stability to ideal magnetohydrodynamic ballooning and kink modes. At conventional aspect ratios, it is shown that access to the second regime of ballooning stability is facilitated by moderate squareness. In a low aspect rat...
Characteristics of the H-mode pedestal are studied in Type I ELM discharges with ITER cross-sectional shape and aspect ratio. The scaling of the width of the edge steep gradient region, δ, which is most consistent with the data are with the normalized edge pressure, (βPEDPOL)0.4. Fits of δ to a function of temperature, such as ρPOL, are ruled out i...
The peeling mode restricts access to the second stability region of the ideal ballooning mode at the tokamak plasma edge. Using a two-dimensional, high toroidal mode number eigenmode code employing a model tokamak equilibrium, it is shown that a window to second stability exists for a sufficiently deep magnetic well. The different mode structures o...
The H-mode confinement enhancement factor, H, is found to be strongly correlated with the height of the edge pressure pedestal in ITER shape discharges. In discharges with type I edge-localized modes (ELMs) the pedestal pressure is set by the maximum pressure gradient before the ELM and the width of the H-mode transport barrier. The pressure gradie...
The edge pressure gradient (H-mode pedestal) for computed equilibria in which the current density profile is consistent with the bootstrap current may not be limited by the first-regime ballooning limit. The transition to second stability is easier for higher elongation, intermediate triangularity, larger aspect ratio, pedestal at larger radius, na...
Simultaneous achievement of high energy confinement, tau E, and high plasma beta, beta , leads to an economically attractive compact tokamak fusion reactor. High confinement enhancement, H= tau E/ tau E-ITER89P=4, and high normalized beta beta N beta /(I/aB)=6%-m-T/MA have been obtained in DIII-D experimental discharges. These improved confinement...
Negative central magnetic shear (NCS) discharges with and up to 80% of the current non-inductively driven are reproducibly produced in the DIII-D tokamak. Strong peaking of , plasma rotation and, in some cases, are observed inside the NCS region. Transport analysis shows that the core ion thermal diffusivity is substantially reduced and near the ne...
The characteristics of the H--mode pedestal are studied in a variety of discharge shapes and plasma conditions on DIII-D. Pedestal characteristics are important in their relation to the overall plasma energy confinement, and to the properties of edge localized modes (ELMs). The width of the H--mode transport barrier was found to be relatively indep...
Edge instabilities with moderate toroidal mode numbers n=2--5 typically terminate the ELM-free phase of DIII--D high performance discharges with a fast growth time gamma-1≈20--150 mus. These moderate n magnetic precursors were also observed, although less frequently, in the ELMing phase. Ideal stability calculations of the experimental equilibri...
The energy and momentum loss resulting from ELMs is typically sufficient to destroy or prevent formation of the internal transport barriers that result in improved confinement in VH and NCS-type discharges. In DIII-D experiments, decreased ELM amplitude has been obtained by reducing access to the ballooning mode 2nd stable regime in the discharge e...
Recent advances in tokamak physics indicate that a spherical tokamak may offer a magnetic fusion development path that can be started with a small size pilot plant and progress smoothly to larger power plants. Full calculations of stability to kink and ballooning modes show the possibility of greater than 50% β-toroidal with the normalized β [βN=βT...
A new formalism for analyzing the magnetohydrodynamic stability of a limiter tokamak edge plasma is developed. Two radially localized, high toroidal mode number n instabilities are studied in detail: a peeling mode and an edge ballooning mode. The peeling mode, driven by edge current density and stabilized by edge pressure gradient, has features wh...
A tokamak equilibrium model, local to a flux surface, is introduced which is completely described in terms of nine parameters including aspect ratio, elongation, triangularity, and safety factor. By allowing controlled variation of each of these nine parameters, the model is particularly suitable for localized stability studies such as those carrie...
Recent calculations based on improved equilibrium reconstructions for DIII--D ELMing H--mode discharges with steep edge pressure gradients show a clear correlation between observed Type I ELMs and the prediction of unstable strongly edge localized ideal MHD intermediate n>3 modes. Since discovery of the H--mode and the associated ubiquitous edge lo...
The low-aspect-ratio tokamak or spherical torus (ST) approach offers the two key elements needed to enable magnetic confinement fusion to make the transition from a government-funded research program to the commercial marketplace: a low-cost, low-power small-size market entry vehicle and a strong economy of scale in larger devices. Within the ST co...
![Fig. 1. LAR power plant core [1998 MW(e)].](profile/Clement-Wong-3/publication/3752438/figure/fig1/AS:668963168088064@1536504656000/LAR-power-plant-core-1998-MWe_Q320.jpg)
A scoping design code has been prepared and utilized to evaluate
the critical issues of the low aspect ratio (LAR) concept as a design
for a fusion power reactor. The physics basis for the A=1.4, κ=3,
β<sub>T</sub> of 62% and bootstrap fraction of 87% equilibrium
design point was derived from earlier work. Using Kr to enhance the
radiation from the...
For the Advanced Tokamak (AT) the requirement of good confinement and high beta leads naturally to large pressure gradients associated with transport barriers. If good bootstrap current alignment is also required, the large current density and pressure gradient result in a fundamental conflict with MHD stability at high beta. Physics solutions for...
Tokamak-based fusion power plant designs rely on ~100% bootstrap current for minimum auxiliary power steady-state operation. Further, noninductive current initiation and ramp-up is an essential feature of ST designs and would simplify the design of any tokamak. DIII--D has begun a study of the ramp-up and control of high-bootstrap-fraction plasmas....
The performance of DIII--D high perfomance discharges with an H--mode edge is often limited by edge instabilities driven by the large edge pressure gradient and the associated large edge bootstrap current density. The instabilities are often preceded by a magnetic perturbation with toroidal mode number n>1 and a fast growth time gamma-1=20-150 mu s...
Ballooning Mode limits on the local pressure gradient near the edge of a plasma are of interest for at least two reasons: stability to ballooning modes at the edge of H--mode plasmas is at least a component of various models attempting to explain ELM behavior and (2) the sensitivity of ``stiff'' transport models to the magnitude of the edge pressur...
The maximum beta that can be sustained for periods of time comparable to
the resistive diffusion time, the so-called long-pulse beta-limit, is
determined by the stability threshold for the tearing mode. A key
parameter in all the theories aiming to determine this threshold is the
Δ' index. This index describes the free energy available for the
mode...
Steady state tokamak equilibria without current drive are found. This is made possible by including the potato bootstrap current close to the magnetic axis. Tokamaks with this class of equilibria do not need seed current or current drive, and are intrinsically steady state. {copyright} {ital 1997} {ital The American Physical Society}
Discharges with negative central magnetic shear (NCS) hold the promise of enhanced fusion performance in advanced tokamaks. However, stability to long wavelength magnetohydrodynamic modes is needed to take advantage of the improved confinement found in NCS discharges. The stability limits seen in DIII-D [J. L. Luxon and L. G. Davis, Fusion Technol....
In spherical tokamaks (ST), the magnetic field strength varies over a wide range across the plasma, and at high betas it deviates significantly from the 1/R dependence of conventional tokamaks. This, together with the high density expected in ST, poses challenging problems for RF heating and current drive. In this paper, we investigate the various...
Warm plasma refraction effects on wave propagation and absorption are examined in the context of a slab model in the parameter regime of interest to the upcoming 110 GHz electron cyclotron heating and current drive experiments on DIII-D.
Low aspect ratio tokamaks (LATs) can potentially provide a high ratio of plasma pressure to magnetic pressure beta and high plasma current I at a modest size. This opens up the possibility of 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 curren...
The low aspect ratio takamak or spherical torus (ST) approach offers the two key elements needed to enable magnetic confinement fusion to make the transition from a government-funded research program to the commercial marketplace: a low cost, low power, small size market entry vehicle and a strong economy of scale in larger devices. Within the ST c...
The low aspect ratio tokamak or spherical torus (ST) approach offers the two key elements needed to enable magnetic confinement fusion to make the transition from a government-funded research program to the commercial marketplace: a low cost, low power, small size market entry vehicle and a strong economy of scale in larger devices. Within the ST c...
High performance discharges having a broad region of weak or slightly negative magnetic shear are observed in DIII--D. They are characterized by a broad pressure profile, enhanced stability and confinement, and high fusion reactivity. Values of betaN ~ 5 and H ~ 4 have been obtained Simultaneously. This enhanced stability and confinement arises fro...
Performance in transiently generated high beta Negative Central Shear (NCS) discharges in DIII--D is limited by MHD instabilities. With L--mode edge conditions, the uncontrolled density peaking results in catastrophic MHD disruptions near beta_N ~2. With a transition to H--mode prior to disruption, higher peak beta can be reached, but the steady-st...
In recent quasi steady-state experiments with low plasma density and high temperature, the maximum achievable beta has been observed to fall substantially below the ideal MHD (Troyon) limit. These experimental data supports the interpretation that tearing modes set limits to the beta value, and agree with theoretical predictions that bootstrap curr...
Both the steady-state advanced tokamak reactor (AT) and the low aspect ratio tokamak reactor (LAT) will require a large fraction of neoclassical bootstrap current to maintain plasma equilibrium. In addition to only modest auxiliary current drive requirements, these bootstrap-current driven tokamaks are characterized by a plasma current profile peak...
Resistive interchange modes can be driven unstable by large pressure gradients in the negative central magnetic shear (NCS) region of advanced tokamaks. Localized stability analysis reveals that the resistive interchange stability criterion (D-R less than or equal to 0) is violated in this region, and unstable n = 1 localized resistive magnetohydro...
Fusion power has been increased by a factor of 3 in DIII-D by tailoring the pressure profile to avoid the kink instability in H-mode plasmas. The resulting plasmas are found to have neoclassical ion confinement. This reduction in transport losses in beam-heated plasmas with negative central shear is correlated with a dramatic reduction in density f...
‘‘Pressure driven tokamaks’’ are special tokamaks for which the rate of injection of energy and mass (e.g., by neutral beams) is so large that no drive for the toroidal current is needed. Examples of pressure driven tokamak equilibria are found numerically; for these examples, both the poloidal and the toroidal magnetic fields vanish in a region ar...
The confinement and the stability properties of the DIII‐D tokamak [Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159] high‐performance discharges are evaluated in terms of rotational and magnetic shear, with an emphasis on the recent experimental results obtained from the...
Stabilization of magnetohydrodynamic ballooning modes by sheared toroidal rotation is demonstrated using a shifted circle equilibrium model. A generalized ballooning mode representation is used to eliminate the fast Alfvén wave, and an initial value code solves the resulting equations. The s−α diagram (magnetic shear versus pressure gradient) of ba...
The effect of a subsonic toroidal flow on the linear magnetohydrodynamic stability of a tokamak plasma surrounded by an external resistive wall is studied. A complex non-self-adjoint eigenvalue problem for the stability of general kink and tearing modes is formulated, solved numerically, and applied to high {beta} tokamaks. Results indicate that to...
An upper bound and a lower bound of the effective trapped particle fraction, {ital f}{sub {ital t}}, in general tokamak equilibria are constructed by invoking the Schwartz inequality. A weighted average of these bounds that is easily evaluated is shown to give an accurate estimate of {ital f}{sub {ital t}} over a wide range of equilibrium parameter...
In the usual matching condition for resistive tearing modes between an inner resistive layer and an outer ideal region, the inertia of the outer region is ignored; that is, the growth rate Q is set equal to zero in the outer region. However, in the large growth rate limit of these modes, the inertia plays a significant role throughout the inner lay...
The effect of a subsonic toroidal flow on the linear magnetohydrodynamic stability of a tokamak plasma surrounded by an external resistive wall is studied. A complex non-self-adjoint eigenvalue problem for the stability of general kink and tearing modes is formulated, solved numerically, and applied to high {beta} tokamaks. Results indicate that to...
The purpose of this note is to quantitatively study the asymptotic behavior of the dipole magnetic field in the tail region of a paraboloidal or cylindrical model of the magnetosphere, assuming the complete screening of the internal field by magnetopause currents. This screening assumption is equivalent to imposing the boundary condition that the n...
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
c...
In this paper a simple one‐dimensional model problem is treated as a paradigm for understanding the nature of rotational shear stabilization in toroidal geometry and its numerical representation. The model is first formulated in a ballooning mode angle θ0 space, where the convective nature of the stabilization is clear. If θ0 is treated as a contin...
Chain terminator sequencing is usually performed on single-stranded DNA. We propose a technique to determine a DNA sequence by sequencing both strands of a double strand in two four-lane gels. The first set of four lanes will contain a superposition of sequence information from the two complementary strands. The second set of four lanes will contai...
A negative potential in the edge region of a tokamak plasma may induce a transition from L-mode to H-mode confinement. Such a negative potential may be produced by injection of various atomic species via edge localized neutral beams, with subsequent prompt loss of ions.
It is shown that a steady-state current can be sustained by the injection of wave helicity. In generalizing to waves of arbitrary polarizations and damping directions, the wave helicity has to include both a magnetic and a kinetic component. A physical picture is presented describing competing effects on current generation, and a generalized helici...
For ω≪Ωi, where Ωi is the ion cyclotron frequency, circularly polarized waves can drive current far exceeding the current resulting from linearly polarized waves. Further, the efficiency can be independent of plasma density. In some cases, this circular polarization may be interpreted in terms of helicity injection. For tokamak applications, where...
Current drive via nonresonant interaction between RF waves and plasma is studied by using the kinetic wave analysis and computation in a stationary state. The nonresonant interaction generates a force, in addition to the usual ponderomotive force. The force of our concern mainly acts as an internal force among plasma species; the net momentum input...
The ac helicity effect discussed by Schalit and Bellan does not impact the current drive efficiency obtained by Ohkawa.
ONETWO is a one-and-a-half-dimensional, time dependent computer code for
modeling plasma transport in Tokamaks. Both circular and noncircular
cross section plasmas, including doublets, are modeled along with
currents in field shaping coils. Electrons, several species of ions, and
two species of neutrals are considered simultaneously. The electrons...
High-..beta.. equilibria which are stable to all ideal MHD modes are found by optimizing the plasma shape and current profile for doublets, up-down asymmetric dees, and symmetric dees. The ideal MHD stability of these equilibria for low toroidal mode number n is analyzed with a global MHD stability code, GATO. The stability to high-n modes is analy...
A numerical technique is used to optimize the shape of tokamak plasmas to achieve maximum stable volume-averaged beta with respect to ballooning modes. Dee shapes with moderately peaked current profile, poloidal beta = 1, and R/a = 2.76 are examined. The optimal shape is a strongly modified dee with a large indentation on the inside edge of the pla...
Understanding and controlling the edge stability of a tokamak is important for optimizing tokamak performance. Stability determines the maximum sustainable pressure gradient at the edge and is believed to be responsible, at least in part, for ELM behavior. The sensitivity of "stiff" transport models to the magnitude of the edge pressure pedestal ha...
Theoretical study and experimental observations suggest that rotation can play a crucial role in determining plasma stability. Since conventional magnetohydrodynamic (MHD) analysis ignores rotation, more advanced computational tools are being developed to confirm the theoretical understanding and to perform comparison between theory and experiment....
The purpose of this research was to better understand tearing and reconnection in genuinely three-dimensional configurations. The authors have identified an equilibrium model that should contain the required features. Three papers have been written and a fourth is in preparation. They are listed in the bibliography.
Gyrofluid simulations of ion temperature gradient (ITG) transport in the ballooning mode representation(R.E. Waltz et al.), Phys. Plasmas 2 (1995) 2408. are extended to general geometry tokamaks. Previous treatments of plasma flux surface shape have been organized about surface by surface analysis of global MHD equilibria making it difficult to iso...
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} â¼ (5a²B{sub t}/RqÏ) [(1 + κ²)/2] [A/(A - 1)] where A {quadruple_bond} R/a which was derived from equilibriu...
We describe the results of the Tokamak Physics Experiment (TPX) Scenario Modeling task. We investigated the achievement of high performance advanced tokamak operating modes in TPX through current and pressure profile shaping using fast wave (FW), lower hybrid (LH), and neutral beam (NB) heating and current drive capabilities. As part of the task, t...
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 magn...
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 equi...
The authors have shown a correlation between the H-mode pressure pedestal height and the energy confinement enhancement in ITER shape discharges on DIII-D which is consistent with the behavior of H in different ELM classes. The width of the steep gradient region was found to equally well fit the scalings δ/R â (Ï{sub POL}/R)²³ and δ/R â (β{...
Due to space limitations at the central column of low aspect ratio tokamaks (LAT), transformerless operation of the LAT tokamaks will be highly desirable. Also the large magnetic well in LATs gives rise to a large trapped particle fraction which renders conven- tional non-inductive current drive schemes inefficient. In this work we examine the use...
Citations
... The spherical tokamak in comparison with the conventional tokamak can operate at high beta (β ≈ 1) while its aspect ratio is also smaller [17,18]. By evacuating all non-essential components such as inboard blanket or shield, OH heating solenoid and inboard poloidal coil from the inner side of the plasma, the size of a tokamak power core can be minimized [19,20]. Research on spherical tokamak has shown the importance of shape and elongation as critical issues. ...
... Solenoid-free plasma initiation and handoff to non-inductive current drive sustainment is a longstanding issue directly relevant to the viability of nuclear-grade STs [11][12][13] that has been consistently recognized in the scientific literature and strategic/community planning documents. Due to the low-geometry of STs, this issue is more pronounced with respect to conventional tokamaks. ...
... to explore the high field (2-3 T), which is indicated by the ULART reactor studies [98]. 4) to try a large additional heating on an ULART. ...
... Such instabilities generate circularly polarized fluctuations with a handedness consistent with the magnetic helicity of the driving electron beam [42]. The circularly polarized fluctuations similarly have net helicity which can drive current [43,44]. ...
... Type III ELMs have been observed both at high collisionality 9,10 and low collisionality. [11][12][13] In both cases, Type III ELMy regime appears when the edge pedestal pressure is relatively low. In several tokamaks such as DIII-D 14 and JET, 15 an ideal ballooning analysis shows that the edge pressure gradient is significantly below the ideal ballooning limit. ...
... Using the CURRAY ray tracing code [30], we have demonstrated that LFFW is capable of driving currents on axis in a single radial pass of the wave power. A previous theoretical work [28] found that the fraction of power absorbed at the Alfven resonance near the outboard edge to be negligible. In a case modeling study using an A 0/ 1.6 equilibrium, we set f0/8.5 MHz and N 0/2.0, and launch the fast wave from above the outboard midplane. ...
![[object Object]](https://i1.rgstatic.net/ii/profile.image/346089048821765-1459525467837_Q64/Scott-Chiu-4.jpg)
... Such magnetic turbulence is generally invoked as a mechanism for magnetic relaxation [10]. Additionally, Alfvénic turbulence exhibits an inverse cascade of magnetic helicity from small to large scales [11,23,24], and coherent beating of fluctuation activity can drive net largescale dc current via the dynamo effect [25][26][27][28]. ...
... Note that the synchrotron radiation driven current will be localized in the region where β 0 is substantially lower than 1, and thus in the gradient region, where the bootstrap current is located. Moreover, since for β 0 ≥ 1 the toroidal current vanishes onaxis, there is no need for a seed current [12]. If a fraction φ a of the radiated power is made asymmetric in N , then I CD = η CD φ a P R /(n e R 0 ) and I CD ≤ 20 MA is obtained for φ a ≤ 10%, so that the fraction of radiated power that has to be made asymmetric is indeed small. ...
... The unstable mode numbers agree with the Mirnov coil observations of the type I ELM precursors [5]. Similar results were obtained at DIII-D for peeling modes associated with ELMs [6]. ...
... where the I B and I φ are the energy integral in the form of I B =´Ê 2 k (exp(−Ê k ))R l dÊ k and I φ =Ê 3/2 k (exp(−Ê k ))R l dÊ k , respectively. Two points need to be emphasized: (1) since the bounce frequency of trapped electrons ω be is independent of the sign of the parallel velocity, the integral termP e,A = 0 is cancelled in the sign summation of σ; (2) considering that the trapped electron fraction f t [56] is affected by plasma collision rate and effective charge number, denoted as the effective trapped electron fraction f t33 [42,43], the ratio between them is c f = f t33 /f t . Then, taking the collision effect into account, the kinetic perturbation of pressure due to the trapped electrons could be empirically reduced by a ratio of the trapped fraction and expressed as P e,K = c fPe,φ . ...
