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The stability of toroidicity‐induced Alfven eigenmodes (TAE) is investigated in general tokamak equilibria with finite aspect ratio and finite plasma beta. The finite orbit width of the hot particles and the collisional damping of the trapped electrons are included. For the trapped hot particles, the finite orbit width is found to be stabilizing. For the circulating hot particles, the finite orbit width effect is stabilizing for larger values of vh/vA (≳1) and destabilizing for smaller values of vh/vA (

The complete ion cyclotron range of frequency (ICRF) heating system for the Tokamak Fusion Test Reactor (TFTR) [Fusion Tech. 21, 1324 (1992)], consisting of four antennas and six generators designed to deliver 12.5 MW to the TFTR plasma, has now been installed. Recently a series of experiments has been conducted to explore the effect of ICRF heating on the performance of low recycling, supershot plasmas in minority and nonresonant electron heating regimes. The addition of up to 7.4 MW of ICRF power to full size (R∼2.6 m, a∼0.95 m), helium‐3 minority, deuterium supershots heated with up to 30 MW of deuterium neutral‐beam injection has resulted in a significant increase in core electron temperature (ΔTe=3–4 keV). Simulations of equivalent deuterium–tritium (D–T) supershots predict that such ICRF heating should result in an increase in βα(0)∼30%. Direct electron heating has been observed and has been found to be in agreement with theory. The ICRF heating has also been coupled to neutral‐beam heated plasmas f...

The stability of high-n toroidicity-induced shear Alfven eigenmodes (TAE) in the presence of fusion alpha particles or energetic ions in tokamaks is investigated. The TAE modes are discrete in nature and thus can easily tap the free energy associated with energetic particle pressure gradient through wave particle resonant interaction. A quadratic form is derived for the high-n TAE modes using gyro-kinetic equation. The kinetic effects of energetic particles are calculated perturbatively using the ideal MHD solution as the lowest order eigenfunction. The finite Larmor radius (FLR) effects and the finite drift orbit width (FDW) effects are included for both circulating and trapped energetic particles. It is shown that, for circulating particles, FLR and FDW effects have two opposite influences on the stability of the high-n TAE modes. First, they have the usual stabilizing effects by reducing the wave particle interaction strength. Second, they also have destabilizing effects by allowing more particles to resonate with the TAE modes. It is found that the growth rate induced by the circulating alpha particles increase linearly with toroidal mode number n for small {kappa}{sub {theta}}{rho}{sub {alpha}}, and decreases as 1/n for {kappa}{sub {theta}}{rho}{sub {alpha}} {much gt} 1. The maximum growth rate is obtained atmore » {kappa}{sub {theta}}{rho}{sub {alpha}} on the order of unity and is nearly constant for the range of 0.7 < {upsilon}{sub {alpha}}/{upsilon}{sub A} < 2.5. On the other hand, the trapped particle response is dominated by the precessional drift resonance. The bounce resonant contribution is negligible. The growth rate peaks sharply at the value of {kappa}{sub {theta}}{rho}{sub {alpha}} such that the precessional drift resonance occurs for the most energetic trapped particles. The maximum growth rate due to the energetic trapped particles is comparable to that of circulating particles.« less

The wave structures, eigenfrequencies and damping rates of toroidicity and ellipticity induced Alfven eigenmodes (TAEs, EAEs) of low toroidal mode numbers (n) are calculated for various axisymmetric ideal MHD equilibria with the global wave finite element code LION. The importance of the safety factor (q) and density (ρ) profiles on the continuum damping rates is analysed. For realistic profiles, several continuum gaps, exist in the plasma discharge. Frequency misalignment of these gaps yields continuum damping rates γ/ω of the order of a few per cent. Finite poloidal beta lowers the TAE eigenfrequency. For beta values below the Troyon limit, the TAE enters the continuum and can thus be stabilized. Finite elongation allows the EAE to exist, but triangularity can have a stabilizing effect through coupling with the continuum. The localization of TAE and EAE eigenfunctions is found to increase with the shear and with n. Therefore, large shear, through enhanced Landau and collisional damping, is a stabilizing factor for TAEs and EAEs

Alpha healing, alpha containment, and alpha stabilization effects are studied in the fusion ignition experiment IGNITEX. The IGNITEX device offers the possibility of producing fusion-ignited plasma...

Intense axisymmetric oscillations driven by suprathermal ions injected in the direction counter to the toroidal plasma current are observed in the DIII-D tokamak. The modes appear at nearly half the ideal geodesic acoustic mode frequency, in plasmas with comparable electron and ion temperatures and elevated magnetic safety factor (qmin 2). Strong bursting and frequency chirping are observed, concomitant with large (10%-15%) drops in the neutron emission. Large electron density fluctuations (ne/ne1.5%) are observed with no detectable electron temperature fluctuations, confirming a dominant compressional contribution to the pressure perturbation as predicted by kinetic theory. The observed mode frequency is consistent with a recent theoretical prediction for the energetic-particle-driven geodesic acoustic mode. © 2008 The American Physical Society.

A new energetic particle-induced Geodesic Acoustic Mode (EGAM) is shown to exist. The mode frequency, mode structure, and mode destabilization are determined non-perturbatively by energetic particle kinetic effects. In particular the EGAM frequency is found to be substantially lower than the standard GAM frequency. The radial mode width is determined by the energetic particle drift orbit width and can be fairly large for high energetic particle pressure and large safety factor. These results are consistent with the recent experimental observation of the beam- driven n=0 mode in DIII-D. The new mode is important since it can degrade energetic particle confinement as shown in the DIII-D experiments. The new mode may also affect the thermal plasma confinement via its interaction with plasma micro-turbulence.

A simple fusion experiment for the production and control of deuterium-tritium-ignited plasmas for scientific study is considered. The basic elements of fusion product alpha-particle behavior at ig...

Reference CRPP-ARTICLE-1990-004View record in Web of Science Record created on 2008-04-16, modified on 2017-05-12

A high‐n WKB‐ballooning mode equation is employed to study toroidicity‐induced shear Alfven eigenmodes (TAE) in s‐α space, where s=(r/q)(dq/dr) is the magnetic shear and α=−(2Rq2/B2)(dp/dr) is the normalized pressure gradient for tokamak plasmas. In the ballooning mode first stability region, TAE modes are found to exist only for α less than some critical value αc. It is found that these TAE modes reappear in the ballooning mode second stability region for bands of α values. The global envelope structures of these TAE modes are studied by the Wentzel–Kramers–Brillouin (WKB) method and are found to be bounded radially if the local mode frequency has a maximum in radius.

I. Introduction (Z. Lin, G. Y. Fu, J. Q. Dong) II. Role of theory and simulation in fusion sciences 1. The Impact of theory and simulation on tokomak experiments (H. R. Wilson, T.S. Hahm and F. Zonca) 2. Tokomak Transport Physics for the Era of ITER: Issues for Simulations (P.H. Diamond and T.S. Hahm) III. Status of fusion simulation and modeling 1. Nonlinear Governing Equations for Plasma Simulations (T. S. Hahm) 2. Equilibrium and stability (L.L. Lao, J. Manickam) 3. Transport modeling (R.E. Waltz) 4. Nonlinear MHD (G.Y. Fu) 5. Turbulence (Z. Lin and R.E. Waltz) 6. RF heating and current drive (D.A. Batchelor) 7. Edge physics Simulations (X.Q. Xu and C.S. Chang) 8. Energetic particle physics (F. Zonca, G.Y. Fu and S.J. Wang) 9. Time-dependent Integrated Modeling (R.V. Budny) 10. Validation and verification (J. Manickam) IV. Major initiatives on fusion simulation 1. US Scientific Discovery through Advanced Computing (SciDAC) Program & Fusion Energy Science (W. Tang) 2. EU Integrated Tokamak Modelling (ITM) Task Force (A. Becoulet) 3. Fusion Simulations Activities in Japan (A. Fukuyama, N. Nakajima, Y. Kishimoto, T. Ozeki, and M. Yagi) V. Cross-disciplinary research in fusion simulation 1. Applied mathematics: Models, Discretizations, and Solvers (D.E. Keyes) 2. Computational Science (K. Li) 3. Scientific Data and Workflow Management (S. Klasky, M. Beck, B. Ludaescher, N. Podhorszki, M.A. Vouk) 4. Collaborative tools (J. Manickam)

A new wave particle resonance mechanism is found explaining the first-orbit prompt neutral beam-ion losses induced by shear Alfven Eigenmodes (AEs) in the DIII-D tokamak. Because of the large banana width, a typical trapped beam ion can only interact locally with a core localised Alfven Eigenmode for a fraction of its orbit, i.e. part of its inner leg of the banana orbit. These trapped beam ions can experience substantial radial kick within one bounce as long as the phases of the wave seen by the particles are nearly constant during this local interaction. A wave particle resonant condition is found based on the locally averaged particle orbit frequencies over the interaction part of the particle orbit. It is further found that the frequency width of the local resonance is quite large because the interaction time is short. This implies that particles over a considerable region of phase space can interact effectively with the localised AEs and experience large radial kicks within one bounce orbit. The radial kick size is found numerically and analytically to scale linearly in AE amplitude and is about 5 cm for typical experimental parameters. These results are consistent with experimental measurement.

Some neutral-beam ions are deflected onto loss orbits by Alfven eigenmodes on their first bounce orbit. The resonance condition for these ions differs from the usual resonance condition for a confined fast ion. Estimates indicate that particles on single-pass loss orbits transfer enough energy to the wave to alter mode stability.

In DIII-D sawteething plasmas, long-lived (1,1) kink modes are often observed between sawtooth crashes. The saturated kink modes have two distinct frequencies. The mode with higher frequency transits to a fishbone-like mode with sufficient on-axis neutral beam power. In this work, hybrid simulations with the global kinetic-magnetohydrodynamic (MHD) hybrid code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of the n = 1 mode with effects of energetic beam ions for a typical DIII-D discharge where both saturated kink mode and fishbone were observed. Linear simulation results show that the n = 1 internal kink mode is unstable in MHD limit. However, with kinetic effects of beam ions, a fishbone-like mode is excited with mode frequency about a few kHz depending on beam pressure profile. The mode frequency is higher at higher beam power and/or narrower radial profile consistent with the experimental observation. Nonlinear simulations have been performed to investigate mod...

Energetic particle modes and Alfven eigenmodes driven by super-Alfvenic fast ions are routinely observed in neutral beam heated plasmas on the National Spherical Torus eXperiment (NSTX). These modes can significantly impact fast ion transport and thus cause fast ion redistribution or loss. Self-consistent linear simulations of Toroidal Alfven Eigenmodes (TAEs) in NSTX plasmas have been carried out with the kinetic/magnetohydrodynamic hybrid code M3D-K using experimental plasma parameters and profiles including plasma toroidal rotation. The simulations show that unstable TAEs with n=3,4, or 5 can be excited by the fast ions from neutral beam injection. The simulated mode frequency, mode radial structure, and phase shift are consistent with measurements from a multi-channel microwave reflectometer diagnostic. A sensitivity study on plasma toroidal rotation, safety factor q profile, and initial fast ion distribution is performed. The simulations show that rotation can have a significant destabilizing effect ...

The damping of Toroidal Alfven Eigenmodes in JET plasmas is investigated by using a reduced kinetic model. Typically no significant damping is found to occur near the center of the plasma due to mode conversion to kinetic Alfven waves. In contrast, continuum damping from resonance near the plasma edge may be significant, and when it is, it gives rise to damping rates that are compatible with the experimental observations.

Toroidal Alfven eigenmodes are shown to be capable of inducing ripple trapping of high‐energy particles in tokamaks, causing intense localized particle loss. The effect has been observed in TFTR [R. Hawryluk, Plasma Phys. Controlled Fusion 33, 1509 (1991)].

The core‐localized toroidicity‐induced Alfven eigenmode (TAE) is shown to exist at finite plasma pressure due to finite aspect ratio effects in tokamak plasma. The new critical beta for the existence of the TAE mode is given by α≊3e+2s2, where e=r/R is the inverse aspect ratio, s is the magnetic shear and α=−Rq2dβ/dr is the normalized pressure gradient. In contrast, previous critical α is given by α≊s2. In the limit of s≪√r/R, the new critical α is greatly enhanced by the finite aspect ratio effects.

Gyrokinetic-magnetohydrodynamic hybrid simulations have been carried out to study the nonlinear saturation of the torodicity-induced Alfv\'en eigenmode driven by energetic particles in a tokamak plasma. It is shown that wave-particle trapping is the nonlinear saturation mechanism for the parameters considered. The corresponding density profile flattening of the hot particles is observed. The saturation amplitude is proportional to the square of the linear growth rate. In addition, a new $n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1,m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ global Alfv\'en eigenmode is shown to be excited by the energetic particles.

The multilevel physics, massively parallel plasma simulation code, M3D, has been used to study spherical tori (STs) and tokamaks. The magnitude of outboard shift of density profiles relative to electron temperature profiles seen in NSTX [National Spherical Torus Experiment] under strong toroidal flow is explained. Internal reconnection events in ST discharges can be classified depending on the crash mechanism, just as in tokamak discharges; a sawtooth crash, disruption due to stochasticity, or high-beta disruption. Toroidal shear flow can reduce linear growth of internal kink. It has a strong stabilizing effect nonlinearly and causes mode saturation if its profile is maintained, e.g., through a fast momentum source. Normally, however, the flow profile itself flattens during the reconnection process, allowing a complete reconnection to occur. In some cases, the maximum density and pressure spontaneously occur inside the island and cause mode saturation. Gyrokinetic hot particle/MHD hybrid studies of NSTX show the effects of fluid compression on a fast-ion-driven n = 1 mode. MHD studies of recent tokamak experiments with a central current hole indicate that the current clamping is due to sawtooth-like crashes, but with n = 0.

Spherical tokamaks, with their relatively low toroidal field, extend fast-ion-driven instability physics to parameter ranges not normally accessed in conventional tokamaks. The low field means that both the fast-ion Larmor radius normalized to the plasma minor radius and the ratio of the fast-ion velocity to the Alfven speed are relatively large. The large Larmor radius of the ions enhances their interaction with instability modes, influencing the structure of the unstable mode spectrum. The relatively large fast-ion velocity allows for a larger population of fast ions to be in resonance with the mode, increasing the drive. It is therefore an important goal of the present proof-of-principle spherical tokamaks to evaluate the role of fast-ion-driven instabilities in fast-ion confinement. This paper presents the first observations of fast-ion losses resulting from toroidal Alfven eigenmodes and a new, fishbone-like, energetic particle mode.

An extended magnetohydrodynamic model including the effect of runaway current is developed and implemented in the M3D code. Based on this model, a simulation has been carried out to investigate the linear stability and the nonlinear evolution of the n = 1 resistive kink mode in the presence of runaway current. It is found that sawteeth oscillation is suppressed in a runaway plasma. The nonlinear evolution of the n = 1 mode only leads to a single sawtooth crash before reaching a new steady state axi-symmetric equilibrium with flattened current profile in the plasma core and q(0)>1.

Compact stellarator configurations have been obtained with good neoclassical confinement that are stable to both pressure- and current-driven modes for high values of beta. These configurations are drift-optimized tokamak-stellarator hybrids with a high-shear tokamak-like rotational transform profile and /B/ that is approximately poloidally symmetric. The bootstrap current is consistent with the required equilibrium current and, while larger than that in existing stellarators, is typically only a small fraction (1/3-1/5) of that in an equivalent tokamak. These configurations have strong magnetic wells and consequently high interchange stability beta limits up to beta=23%. Because of the reduced bootstrap current, these configurations are stable to low-n ideal MHD kink modes with no wall stabilization for values of beta ( approximately 7%-11%) significantly larger than in an equivalent advanced tokamak.

Nonlinear frequency chirping of toroidal Alfen eigenmodes (TAE) driven by energetic particles is investigated by kinetic simulations in toroidal plasmas. It is found that the up–down symmetry of the frequency chirping of a TAE is broken due to an anisotropic pitch-angle distribution with dominant co-passing energetic particles. The nonuniform distribution of the free energy associated with the initial energetic particle distribution causes biased driving forces that result in a strongly asymmetric frequency chirping. The evolution of the perturbed distribution function in the phase space shows that a hole–clump pair moves together towards the magnetic axis for the small pitch-angle parameter cases. The downward chirping of the mode frequency is associated with the negative drift of the phase island in the KAM surfaces or the resonance δf structures in the radial direction. On the other hand, the energetic particle distribution with larger pitch-angle parameters leads to upward chirping of the TAE frequency. The upward chirping is due to the drifting of the resonance structure towards the boundary of the simulation region and overlapping of different poloidal resonances in the (Λ, E) phase space at the late stage. The phase space dynamics provides a key mechanism for understanding the wave chirping direction and particle transport process.

Nonlinear simulations of sawteeth and related energetic particle transport are carried out using the kinetic/magnetohydrodynamic (MHD) hybrid code M3D-K. MHD simulations show repeated sawtooth cycles for a model tokamak equilibrium. Furthermore, test particle simulations are carried out to study the energetic particle transport due to a sawtooth crash. The results show that energetic particles are redistributed radially in the plasma core, depending on pitch angle and energy. For trapped particles, the redistribution occurs for particle energy below a critical value in agreement with existing theories. For co-passing particles, the redistribution is strong with little dependence on particle energy. In contrast, the redistribution level of counter-passing particles decreases with increasing particle energy.

The question of how to proceed toward ever more realistic plasma simulation studies using ever increasing computing power is addressed. The answer presented here is the M3D (Multilevel 3D) project, which has developed a code package with a hierarchy of physics levels that resolve increasingly complete subsets of phase-spaces and are thus increasingly more realistic. The rationale for the multilevel physics models is given. Each physics level is described and examples of its application are given. The existing physics levels are fluid models (3D configuration space), namely magnetohydrodynamic (MHD) and two-fluids; and hybrid models, namely gyrokinetic-energetic-particle/MHD (5D energetic particle phase-space), gyrokinetic-particle-ion/fluid-electron (5D ion phase-space), and full-kinetic-particle-ion/fluid-electron level (6D ion phase-space). Resolving electron phase-space (5D or 6D) remains a future project. Phase-space-fluid models are not used in favor of delta f particle models. A practical and accurate nonlinear fluid closure for noncollisional plasmas seems not likely in the near future.

Resonant Toroidal Alfven Eigenmodes (RTAEs) [1, 2] excited by neutral beam ions are observed in the region of the internal transport barrier in enhanced reverse shear (ERS) plasmas on TFTR. These modes occur in multiples of the same toroidal mode number in the range n=2-4 and appear as highly localized structures near the minimum in the q-profile with frequency near to that expected for TAEs. Unlike regular TAEs, these modes are observed in plasmas where the birth velocity of beam ions is well below the fundamental or sideband resonance condition. Theoretical analysis indicates that the Toroidicity induced Alfven Eigenmode (TAE) does not exist in these discharges due to strong pressure gradients (of the thermal and fast ions) which moves the mode frequency down into the lower Alfven continuum. However a new non-perturbative analysis (where the energetic particles are allowed to modify the mode frequency and mode structure) indicates that RTAEs can be driven by neutral beam ions in the weak magnetic shear region of ERS plasma, consistent with observations on TFTR. The importance of such modes is that they may affect the alpha particle heating profile or enhance the loss of energetic alpha particles in an advanced tokamak reactor wheremore » large internal pressure gradients and reverse magnetic shear operation are required to sustain large bootstrap current.« less

An analytic stability criterion is derived for the vertical mode in a large aspect ratio stellarator. The effects of vacuum magnetic field generated by helical coils are shown to be stabilizing due to enhancement of field line bending energy. For wall at infinite distance from the plasma, the amount of external poloidal flux needed for stabilization is given by f = [k(subscript 2)-K]/[K(subscript 2) + 1] where k is the axisymmetric elongation and f is the ratio of vacuum rotational transform to the total transform.

The effects of pressure gradient on the existence of global Alfven eigenmodes (GAE) in Reversed Field Pinch are studied by numerical calculation. It is found that GAEs near the plasma core can exist when pressure gradient is sufficiently large. The calculated mode frequency and structure are consistent with the experimental results in the Madison Symmetric Torus.

The M3D (Multi-level 3D) tokamak simulation project aims at the simulation of tokamak plasmas using a multi-level tokamak code package. Several current applications using MHD and Extended-MHD models are presented; high-{beta} disruption studies in reversed shear plasmas using the MHD level MH3D code, {omega}{sub *i} stabilization and nonlinear island rotation studies using the two-fluid level MH3D-T code, studies of nonlinear saturation of TAE modes using the hybrid particle/MHD level MH3D-K code, and unstructured mesh MH3D{sup ++} code studies. In particular, three internal mode disruption mechanisms are identified from simulation results which agree well with experimental data.

Alfven modes are excited by energetic ions in TFTR during intense minority ICRF heating. There is a clear threshold in rf power above which the modes are distabilized. The net effect of these modes is the increase of the fast ion losses, with an associated saturation of the ion tail energy and of the efficiency of the heating. Typically, several modes are excited with progressive n-numbers, with frequencies in the neighborhood of 200 kHz. Results suggest that Energetic Particle Modes (EPM), mostly unseen by the Mirnov coils, are generated near the center and are responsible for the ion losses. Stronger global TAE modes, which are destabilized by the stream of displaced fast ions, appear responsible only for minor losses.

Kinetic simulations based on a reduced model are carried out to study dynamic evolutions of multiple toroidicity-induced shear Alfven eigenmodes driven by energetic particles. It is found that passing and trapped particles play quite different roles on the mode evolution. For cases without background damping, passing particles lead to a longer linear growth phase and subsequent enhancement of the nonlinear saturation level when resonant regions with two modes are closely overlapped. On the other hand, trapped particles are mainly responsible for the persistent mode growth in the nonlinear phase. By comparing the results from anisotropic and isotropic simulations, it is suggested that passing particles have a negative impact on the mode development in the nonlinear phase. For the near marginal stability cases with large background damping, the upward and downward frequency chirping in multiple branches are significantly affected by the multi-mode interaction due to overlapping of hole and clump in the distribution function.

Extensive linear and nonlinear simulations have been carried out to investigate the energetic particle-driven fishbone instability in spherical tokamak plasmas with weakly reversed q profile and the qmin slightly above unity. The global kinetic-MHD hybrid code M3D-K is used. Numerical results show that a fishbone instability is excited by energetic beam ions preferentially at higher qmin values, consistent with the observed appearance of the fishbone before the “long-lived mode” in MAST and NSTX experiments. In contrast, at lower qmin values, the fishbone tends to be stable. In this case, the beam ion effects are strongly stabilizing for the non-resonant kink mode. Nonlinear simulations show that the fishbone saturates with strong downward frequency chirping as well as radial flattening of the beam ion distribution. An (m, n) = (2, 1) magnetic island is found to be driven nonlinearly by the fishbone instability, which could provide a trigger for the (2, 1) neoclassical tearing mode sometimes observed after the fishbone instability in NSTX.

Plasmas in spherical and conventional tokamaks, with weakly reversed shear q profile and minimum q above but close to unity, are susceptible to an non-resonant (m,n) = (1,1) internal kink mode. This mode can saturate and persist and can induce a (2,1) seed island for Neoclassical Tearing Mode. [Breslau et al. Nucl. Fusion 51, 063027 (2011)]. The mode can also lead to large energetic particle transport and significant broadening of beam-driven current. Motivated by these important effects, we have carried out extensive nonlinear simulations of the mode with finite toroidal rotation using parameters and profiles of an NTSX plasma with a weakly reversed shear profile. The numerical results show that, at the experimental level, plasma rotation has little effect on either equilibrium or linear stability. However, rotation can significantly influence the nonlinear dynamics of the (1,1) mode and the induced (2,1) magnetic island. The simulation results show that a rotating helical equilibrium is formed and maintained in the nonlinear phase at finite plasma rotation. In contrast, for non-rotating cases, the nonlinear evolution exhibits dynamic oscillations between a quasi-2D state and a helical state. Furthermore, the effects of rotation are found to greatly suppress the (2,1) magnetic island even at a low level.

A kinetic simulation code based on a reduced model is developed to study dynamic evolutions of a single toroidicity-induced shear Alfven eigenmode driven by energetic particles. For zero background damping, it is found that the wave amplitude in nonlinear phase can either saturate for weak energetic particle drives or slowly increase for strong drives. This slow nonlinear growth in strong drive cases is found to be associated with broadening and overlapping of resonances between the wave and trapped particles. For the near-marginal-stability case with a large background damping, the mode nonlinear evolution exhibits strong upward and downward frequency chirping in multiple branches. A hole/clump formation is observed clearly in the corresponding evolution of energetic particle distribution.

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 Alfvén 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. © 2013 IOP Publishing Ltd.

A peak fusion power production of 9.3±0.7 MW has been achieved on the Tokamak Fusion Test Reactor (TFTR) in deuterium plasmas heated by co and counter injected deuterium and tritium neutral beams with a total power of 33.7 MW. The ratio of fusion power output to heating power input is 0.27. At the time of the highest neutron flux the plasma conditions are: Te(0)=11.5 keV, Ti(0)=44 keV, ne(0)=8.5×1019 m−3, and 〈Zeff〉=2.2 giving τE=0.24 s. These conditions are similar to those found in the highest confinement deuterium plasmas. The measured D‐T neutron yield is within 7% of computer code estimates based on profile measurements and within experimental uncertainties. These plasmas have an inferred central fusion alpha fraction of 0.2% and central fusion power density of 2 MW/m3 similar to that expected in a fusion reactor. Even though the alpha velocity exceeds the Alfven velocity throughout the time of high neutron output in most high power plasmas, MHD activity is not substantially different from that in co...

Chirping toroidicity-induced Alfvén eigenmodes (TAEs) are destabilized during neutral beam injection on the National Spherical Torus Experiment (NSTX (Ono M. et al 2000 Nucl. Fusion 40 557)) by super-Alfvénic ions with velocities up to five times larger than the Alfvén velocity. TAEs exhibit repeated bursts in amplitude and down-chirps in frequency. Larger bursts, so-called TAE avalanches, are eventually observed and correlate with a loss of fast ions up to 30% over ∼1 ms. Frequency, amplitude and radial structure of TAEs are characterized via magnetic pickup coils and a multi-channel reflectometer system. The modes have a broad radial structure, which appears to be unaffected by the large frequency and amplitude variations. However, the large mode amplitude does impact the modes' dynamics by favouring the coupling among different modes. In addition, the coupling involves kink-like modes and can therefore degrade the thermal plasma confinement. In spite of the non-linear regime characterizing the TAE dynamics, the measured properties are found to be in reasonable agreement with solutions from the ideal MHD code NOVA.

The effects of energetic ions on stability of tearing mode are investigated by global kinetic/MHD hybrid simulations in a low beta tokamak plasma. The kinetic effects of counter circulating energetic ions from the non-adiabatic response are found to be strongly destabilizing while the effects from the adiabatic response are stabilizing. The net effect with both adiabatic and non-adiabatic contributions is destabilizing. On the other hand, the kinetic effects of co-circulating energetic ions from the non-adiabatic response are calculated to be weakly stabilizing while the corresponding adiabatic contribution is destabilizing for small energetic ion beta. The net effect is weakly stabilizing. The dependence of kinetic effects on energetic ion beta, gyroradius, and speed is studied systematically and the results agree in large part with the previous analytic results for the kinetic effects of circulating particles. For trapped energetic ions, their effects on tearing mode stability are dominated by the adiabatic response due to large banana orbit width and strong poloidal variation of particle pressure. The net effect of trapped energetic particles on tearing modes is much more destabilizing as compared to that of counter circulating particles at the same beta value.

The Tokamak Fusion Test Reactor (TFTR) has performed initial high-power experiments with the plasma fueled by deuterium and tritium to nominally equal densities. Compared to pure deuterium plasmas, the energy stored in the electron and ions increased by ~20%. These increases indicate improvements in confinement associated with the use of tritium and possibly heating of electrons by α-particles.

Fishbone instabilities, driven by trapped and barely passing energetic particles (EPs), including electrons and ions (EEs or EIs), are numerically studied with the spatial distribution of EPs taken into account. The dispersion relations of the modes are derived for slowing-down and Maxwellian models of EP energy distribution. It is found that the modes with frequency comparable to the toroidal precession frequency ωd of EPs are resonantly excited. Electron and ion fishbone modes share the same growth rates and real frequencies but rotate in opposite directions. The frequency of the modes is found to be higher in the case of near-axis heating than that of off-axis heating. The fishbone instabilities can only be excited by barely trapped or barely passing and deeply trapped particles in positive and negative spatial density gradient regions, respectively. In addition, the most interesting feature of the fishbone modes induced by barely passing particles is that there exists a second stable regime in the higher βh (pressure of EPs/toroidal magnetic pressure) region, and the modes exist in the range of βth1 < βh < βth2 (βth is threshold or critical beta of EPs) only. The results are well confirmed with Nyquist technology. The possible physical mechanism for the existence of the second stable regime is discussed.

Motivated by experimental observations of apparently triggerless tearing modes, we have performed linear and nonlinear MHD analysis showing that a non-resonant mode with toroidal mode number n = 1 can develop in the National Spherical Torus eXperiment (NSTX) at moderate normalized βN when the shear is low and the central safety factor q 0 is close to but greater than one. This mode, which is related to previously identified ‘infernal’ modes, will saturate and persist, and can develop poloidal mode number m = 2 magnetic islands in agreement with experiments. We have also extended this analysis by performing a free-boundary transport simulation of an entire discharge and showing that, with reasonable assumptions, we can predict the time of mode onset.

A hybrid gyrokinetic ions/massless fluid electron model is used to study the stability of high-n toroidal Alfven eigenmodes (TAEs) in ITER [M. Shimada et al., Nucl. Fusion 47, S1 (2007)]. The hybrid model has been implemented in the particle-in-cell turbulence simulation code GEM [Y. Chen and S. E. Parker, J. Comput. Phys. 220, 839 (2007)]. The adequacy of the hybrid model for simulating TAEs has been previously demonstrated [J. Lang et al., Phys. Plasmas 16, 102101 (2009)] by comparing the simulated TAE mode frequency and structure with an eigenmode analysis, and the thermal ion kinetic damping effect with analytic theory. By using a global particle-in-cell code the effects of large orbit width and nonlocal mode structures can be accurately included. Damping rate due to numerical filtering is carefully monitored, and convergence with respect to particle number, grid resolution, etc., is thoroughly tested. The simulations show that the most unstable modes in ITER lie in the rage of 10

The internal kink (fishbone) modes, driven by barely passing energetic ions (EIs), are numerically studied with the spatial distribution of the EIs taking into account. It is found that the modes with frequencies comparable to the toroidal precession frequencies are excited by resonant interaction with the EIs. Positive and negative density gradient dominating cases, corresponding to off- and near-axis depositions of neutral beam injection (NBI), respectively, are analyzed in detail. The most interesting and important feature of the modes is that there exists a second stable regime in higher βh (=pressure of EIs/toroidal magnetic pressure) range, and the modes may only be excited by the barely passing EIs in a region of βth1

An analytic stability criterion is derived for the vertical mode in a large aspect ratio stellarator with uniform current density profile. The effects of vacuum magnetic field generated by helical coils are shown to be stabilizing due to enhancement of field line bending energy. For a wall at infinite distance from the plasma, the amount of external poloidal flux needed for stabilization is given by f=(κ2−κ)/(κ2+1), where κ is the axisymmetric elongation and f is the ratio of vacuum rotational transform to the total transform.

Gyrokinetic δf particle simulation is used to investigate toroidicity-induced Alfven eigenmodes (TAEs). Both thermal ions and energetic particles are fully kinetic, but a reduced fluid model is used for the electrons. Simulation of a single n=2 global TAE is carefully analyzed and benchmarked with an eigenmode analysis, and a very good agreement is achieved in both mode structure and mode frequency. The instability of the mode in the presence of energetic particles is demonstrated. In particular, gyrokinetic simulations demonstrate the kinetic damping effect of thermal ions, where the finite radial structure of kinetic Alfven waves is well resolved and the damping rate is compared to and found to agree well with analytical theory.

A nonperturbative kinetic/magnetohydrodynamics eigenvalue code has been constructed for calculation of kinetic damping of shear Alfven eigenmodes in general tokamak geometry with finite pressure. The model describes shear Alfven waves with kinetic effects from thermal species including thermal ion finite Larmor radius effects and parallel electric field. An analytic formula for the radiative damping of reversed shear Alfven eigenmodes is obtained for tokamak plasmas with reversed shear q profile. Numerical calculations reveal the existence of multiple kinetic reversed shear Alfven eigenmodes (KRSAEs). It is found that the damping rate of the KRSAEs scales linearly with the thermal ion gyroradius. The damping rates are larger for modes with more peaks in the radial structures. These results are consistent with analytic expectation. The KRSAEs found here can be used to interpret the RSAEs frequency sweeping down observed sometime in the tokamak experiments.

The Integrated Plasma Simulator (IPS) provides a framework within which some of the most advanced, massively-parallel fusion modeling codes can be interoperated to provide a detailed picture of the multi-physics processes involved in fusion experiments. The presentation will cover four topics: 1) recent improvements to the IPS, 2) application of the IPS for very high resolution simulations of ITER scenarios, 3) studies of resistive and ideal MHD stability in tokamk discharges using IPS facilities, and 4) the application of RF power in the electron cyclotron range of frequencies to control slowly growing MHD modes in tokamaks and initial evaluations of optimized location for RF power deposition.