Search

Numerical thermalization induced by discrete-particle effects was observed in particle-in-cell (PIC) simulations1, which show that the thermal relaxation time scales with ND2 and ND for one-dimensional (1D) and two-dimensional (2D) models2, respectively. The parameter ND denotes the number of particles in a Debye length (1D) or a Debye square (2D). However, it was found recently that the thermal relaxation time is anomalously shortened to scale with ND while adding the Monte-Carlo collisions in a 1D PIC simulation.3,4 In this work, we examine the numerical thermalization in two-dimensional ES PIC simulations with the consideration of electron-ion collision and electron-neutral collision.4 Our results show that the thermal relaxation time is less sensitive to the collision frequency as compared to the 1D cases, and the thermal relaxation time remains to scale with ND as predicted by the theoretical analysis using the Balescu-Lenard-Landau kinetic theory 5.

The radial profile of the Pfirsch–Schluter current has been measured directly for the first time in a tokamak using motional Stark effect (MSE) polarimetry. The MSE diagnostic measures the vertical component of the magnetic field (Bz) as a function of the plasma major radius. The analysis technique presented here converts the experimental Bz profile into a flux-surface-average current density as well as a local current density. Taking the appropriate difference between these two quantities yields a direct measurement of the Pfirsch–Schluter current density, and consequently a MSE-based measurement of the plasma pressure profile. The bootstrap current density can also be directly determined from the Bz profile (with greater approximation) in the collisionless limit. An equilibrium reconstruction is not required for this MSE analysis technique, although a few basic geometric parameters such as the plasma minor radius, elongation and triangularity need to be known. The usefulness of this approach for analysing the current profile is demonstrated using discharges from the DIII-D tokamak.

Green’s-function techniques are used to calculate electron cyclotron current drive (ECCD) efficiency in general tokamak geometry in the low-collisionality regime. Fully relativistic electron dynamics is employed in the theoretical formulation. The high-velocity collision model is used to model Coulomb collisions and a simplified quasilinear rf diffusion operator describes wave–particle interactions. The approximate analytic solutions which are benchmarked with a widely used ECCD model, facilitate time-dependent simulations of tokamak operational scenarios using the noninductive current drive of electron cyclotron waves.

A class of very high poloidal beta (βp) equilibria is exhibited in which eβp (e 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 aspect ratio configuration, equilibria with eβp=3 exist, which is 50% higher than both the previously observed record and the analytically predicted limit. For very low aspect ratio with e−1=1.4, typical of spherical tori, values of eβp=5 are possible.

Numerical self-heating and thermalization are two unphysical artifacts in particle-in-cell (PIC) simulations due to the implicit assumptions used in the numerical method. Numerical self-heating in plasma simulations can typically be suppressed by using higher order finite-difference methods, field smoothing and particle weighting schemes. On the other hand, numerical thermalization is associated with the granularity of the particles that introduces relaxation in the velocity distribution functions (i.e. the particle velocity distribution approaches Maxwellian). In 2D collisionless plasma simulations, the rate of relaxation has been shown to be proportional to 1/N D , where N D is the number of particles per Debye length1. This scaling has been illustrated to be true in several previous works using electrostatic PIC codes.

Significant progress in obtaining high performance discharges lasting many energy confinement times in the DIII-D tokamak has been realized in recent experimental campaigns. Normalized performance ∼10 has been sustained for more than 5>E with qmin > 1.5. (The normalized performance is measured by the product βNH89, indicating the proximity to the conventional β limits and energy confinement quality, respectively.) These H mode discharges have an ELMing edge and β < 5%. The limit to increasing β is a resistive wall mode, rather than the tearing modes as previously observed. Confinement remains good despite qmin > 1. 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. Measurement of the current density and loop voltage profiles indicate that ≈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 β control, which are essential for operating advanced tokamak discharges, were demonstrated in ELMing H mode discharges with βNH89 ≈ 7 for up to 6.3 s or ≈34τE. These discharges appear to have stationary current profiles with qmin ≈ 1.05 in agreement with the current profile relaxation time ≈1.8 s.

Significant progress has been made in obtaining high-performance discharges for many energy confinement times in the DIII-D tokamak [J. L. Luxon et al., Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159]. Normalized performance (measured by the product of βNH89 and indicative of the proximity to both conventional β limits and energy confinement quality, respectively) ∼10 has been sustained for >5 τE with qmin>1.5. These edge localized modes (ELMing) H-mode discharges have β∼5%, which is limited by the onset of resistive wall modes slightly above the ideal no-wall n=1 limit, with approximately 75% of the current driven noninductively. The remaining Ohmic current is localized near the half-radius. The DIII-D electron cyclotron heating system is being upgraded to replace this inductively driven current with localized electron cyclotron current drive (ECCD). Density control, which is required for effective ECCD, has been successfully demonstrated in long-pulse high-performance ELMing H-mode discharges with βNH89∼7 for up to 6.3 s. In plasma shapes compatible with good density control in the present divertor configuration, the achieved βN is somewhat less than that in the high βNH89=10 discharges.

A new method of current drive analysis is demonstrated that compares the measured pitch angles from motional Stark effect (MSE) spectroscopy with simulations of the expected MSE response to localized ECCD. By comparing simulations of the MSE signals with measurements, the best fit of the ECCD profile is determined. The ECCD efficiency ascertained in this manner decreases as the current drive location moves to larger minor radius owing to electron trapping effects. The ECCD efficiency is shown to be highest when the driven current is on the high magnetic field side of the plasma, as expected from theory. The width of the ECCD profile is also in good agreement with theory; previous reports of a broader than expected ECCD profile are shown to have been caused by insufficient radial resolution of the magnetic equilibrium reconstruction.

The noncanonical Lagrangian theory of guiding center orbits is applied to the coordinate system of White–Chance–Boozer. The result is a generalized set of equations of motion which eliminates certain approximations of the static field and includes the effects of large rotations and high frequency waves. A quasilinear gyrokinetic theory is shown to readily follow from these equations.

The status of modelling work focused on developing the advanced tokamak (AT) scenarios in DIII-D is discussed. The objective of the work is twofold: (a) to develop AT scenarios with ECCD using time dependent transport simulations, coupled with heating and current drive models, consistent with MHD equilibrium and stability; and (b) to use time dependent simulations to help plan experiments and to understand the key physics involved. Time dependent simulations based on transport coefficients derived from experimentally achieved target discharges are used to perform AT scenario modelling. The modelling indicates that off-axis ECCD with approximately 3 MW absorbed power can maintain high performance discharges with qmin > 1 for 5-10 s. The resultant equilibria are calculated to be stable to n = 1 pressure driven modes. The plasma is well into the second stability regime for high-n ballooning modes over a large part of the plasma volume. The role of continuous localized ECCD is studied for stabilizing m/n = 2/1 tearing modes. Progress towards validating current drive and transport models, consistent with experimental results, and developing self-consistent, integrated high performance AT scenarios is discussed.

The equations of motion of charged particles of a strongly magnetized flowing plasma under the influence of high frequency waves are derived in the guiding center approximation. A quasilinear theory of the interactions of waves with rotating plasmas is formulated. This is applied to investigate the effect of radio frequency waves on a rotating tokamak plasma with a heated minority species. The angular momentum drive is mainly due to the rf-induced radial minority current. The return current by the bulk plasma gives an equal and opposite rotation drive on the bulk. Using moment equations and a small banana width approximation, the J×B drive was evaluated for the bulk plasma. Quite remarkably, although collisions are included, the net rotation drive is due to a term which can be obtained by neglecting collisions.

Localized non-inductive currents due to electron cyclotron wave absorption have been measured on the DIII-D tokamak. Clear evidence of non-inductive currents is seen on the internal magnetic field measurements by motional Stark effect spectroscopy. The magnitude and location of the non-inductive current is evaluated by comparing the total and ohmic current profiles of discharges with and without electron cyclotron wave power. The measured current agrees with Fokker-Planck calculations near the magnetic axis, but exceeds the predicted value as the location of the current drive is moved to the half-radius.

Localized currents due to electron cyclotron current drive have been measured for the first time in experiments on the DIII-D tokamak. The location of driven current in the plasma has been varied from near the center of the tokamak out to half of the minor radius. The measured current drive efficiency agrees with quasilinear Fokker-Planck calculations near the center and exceeds the predicted value with increasing minor radius. Reduction of the trapped electron fraction due to finite collisionality is a leading candidate to explain the discrepancy. (c) 1999 The American Physical Society.

Both the dynamic and equilibrium thermal responses of an L?mode plasma to repetitive ECH heat pulses were measured and compared with predictions from several thermal transport models. While no model consistently agreed with all observations, the GLF23 model was most consistent with the perturbed electron and ion temperature responses for one of the cases studied, which may indicate a key role played by electron modes in the core of these discharges. Generally, the IIF and MM models performed well for the perturbed electron response while the GLF23 and IFS/PPPL models agreed with the perturbed ion response for all three cases studied. No single model agreed well with the equilibrium temperature profiles measured.

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 equilibria, these configurations have high bootstrap current fractions (fBS∼50%–70%); they require only modest central current drive for maintaining steady state and are therefore compatible with advanced tokamak (AT) operation. Strong plasma shaping is crucial for achieving the high β and high bootstrap fraction simultaneously.

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 ratio, fully bootstrap current driven spherical torus, optimization of the squareness results in an increase in β of the order of 10%, leading to a configuration stable to ballooning, axisymmetric, and ideal n⩽5 kink modes at β≃67%.

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/MA). Small to moderate improvements in βN result either from broadening the pressure or from strong cross-section shaping. At fixed safety factor the latter translates to a much larger increase in β and the root mean square β denoted as β*. With both optimal profiles and strong shaping, however, the gain in all the relevant fusion performance parameters is dramatic, and β and β* can be increased by a factor of 5. The calculations show that stabilization from a nearby conducting wall greatly contributes to this large improvement, since coupling of the plasma to the wall is increased for the optimum profiles and cross-section. Moreover, the alignment of the bootstrap current density profile with the total current density profile is also optimized with broad pressure, strong cross-section shaping and high βN, thus minimizing steady state current drive requirements. Sensitivity studies using other profiles show some variation in the actual β limits, but the general trends remain robustly invariant.

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/(I/aβ)] as high as 10 and fully aligned 100% bootstrap current. Such β-values coupled with 2–3 T toroidal fields imply a pilot plant about the size of the present DIII-D tokamak could produce ∼800 MW thermal, 160 MW net electric, and would have a ratio of gross electric power over recirculating power (QPLANT) of 1.9. The high β values in the ST mean that E×B shear stabilization of turbulence should be ten times more effective in the ST than in present tokamaks, implying that the required high quality of confinement needed to support such high beta values will be obtained. The anticipated β values are so high that the allowable neutron flux at the blanket sets the device size, not the physics constraints. The ST has a favorable size scaling so that at 2–3 times the pilot plant size the QPLANT rises to 4–5, an economic range and 4 GW thermal power plants result. Current drive power requirements for 10% of the plasma current are consistent with the plant efficiencies quoted. The unshielded copper centerpost should have an adequate lifetime against nuclear transmutation-induced resistance change and the low voltage, high current power supplies needed for the 12-turn TF coil appear reasonable. The favorable size scaling of the ST and the high β mean that in large sizes, if the copper TF coil is replaced with a superconducting TF coil and a shield, the advanced fuel D-He3 could be burned in a device with QPLANT∼4. If the anticipated physics of the ST regime can be proven in near-term experiments and engineering challenges (such as the high power density to be exhausted and centerpost neutronics issues) can be met, then the ST offers the possibility of a magnetic fusion development path with a minimal cost initial step and exciting further possibilities.

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, narrower pedestal width, higher , and lower collisionality.

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 carried out using the ballooning mode representation of the gyrokinetic equations.

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}

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) and low frequency FWCD in LARTs is examined using exact evaluations of the current drive efficiencies from the adjoint technique. The results indicate that the high harmonic ion cyclotron current drive cannot penetrate to the plasma core at the high beta values typical of LART reactors, and hence this scheme may only be applicable for off-axis steady state current drive, while the low frequency current drive penetrates well into the plasma core and is appropriate for on-axis current profile control. The implications for advanced scenarios of LART are discussed

Motional Stark effect polarimetry (MSE) is a well established technique for measuring the magnetic field pitch angle in tokamaks. By viewing the Stark emission spectrum from two different angles, this technique can also provide local measurements of the plasma radial electric field, ${E}_{r}$. Simultaneous measurements of the profiles of magnetic field pitch angle and ${E}_{r}$ are presented for the first time in a high-performance DIII-D tokamak plasma. Direct measurement of ${E}_{r}$ is of great importance in fusion research because the suppression of turbulence through ${\mathbf{E}}_{r}\ifmmode\times\else\texttimes\fi{}\mathbf{B}$ velocity shear provides a mechanism to improve energy confinement.

Negative central magnetic shear (NCS) discharges with {Beta}{sub N} {le} 4, H {le} 3, and up to 80% of the current non-inductively driven are reproducibly produced in the DIII-D tokamak. Strong peaking of T{sub i}, plasma rotation, and in some cases n{sub e} are observed inside the NCS region. Transport analysis shows that the core ion thermal diffusivity is substantially reduced and near the neoclassical value after the formation of the internal transport barrier. The negative central shear is necessary but not sufficient for the formation of this transport barrier. The power required for the formation appears to increase with the toroidal magnetic field. The high performance phase of H-mode NCS discharges often ends with an ELM-like collapse initiated from the edge whereas the L-mode discharges which have a more peaked pressure profile tend to end with a more global n = 1 MHD event.

Reliable operation of discharges with negative central magnetic shear has led to significant increases in plasma performance and reactivity in both low confinement, L‐mode, and high confinement, H‐mode, regimes in the DIII‐D tokamak [Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159]. Using neutral beam injection early in the initial current ramp, a large range of negative shear discharges have been produced with durations lasting up to 3.2 s. The total noninductive current (beam plus bootstrap) ranges from 50% to 80% in these discharges. In the region of shear reversal, significant peaking of the toroidal rotation [fφ(0)∼30–60 kHz] and ion temperature [Ti(0)∼15–22 keV] profiles are observed. In high‐power discharges with an L‐mode edge, peaked density profiles are also observed. Confinement enhancement factors up to H≡τE/τITER‐89P∼2.5 with an L‐mode edge, and H∼3.3 in an edge localized mode (ELM)‐free H mode, are obtained. Transp...

The confinement and the stability properties of the DIII-D tokamak high performance discharges are evaluated in terms of rotational and magnetic shear with emphasis on the recent experimental results obtained from the negative central magnetic shear (NCS) experiments. In NCS discharges, a core transport barrier is often observed to form inside the NCS region accompanied by a reduction in core fluctuation amplitudes. Increasing negative magnetic shear contributes to the formation of this core transport barrier, but by itself is not sufficient to fully stabilize the toroidal drift mode (trapped- electron-{eta}{sub i}mode) to explain this formation. Comparison of the Doppler shift shear rate to the growth rate of the {eta}{sub i} mode suggests that the large core {bold E x B} flow shear can stabilize this mode and broaden the region of reduced core transport . Ideal and resistive stability analysis indicates the performance of NCS discharges with strongly peaked pressure profiles is limited by the resistive interchange mode to low {Beta}{sub N} {lt} 2.3. This mode is insensitive to the details of the rotational and the magnetic shear profiles. A new class of discharges which has a broad region of weak or slightly negative magnetic shear (WNS) is described. The WNS discharges have broader pressure profiles and higher values than the NCS discharges together with high confinement and high fusion reactivity.

‘‘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 around the plasma center. Thus, the ratio between the plasma pressure and the magnetic field pressure is large, namely of order unity. Therefore, pressure driven tokamaks appear attractive for fusion reactors; it is, however, an open question whether there exist magnetohydrodynamically stable pressure driven equilibria.

A weakly relativistic theory of current drive by parallel acceleration of electrons in toroidal geometry is presented. Analytic expressions of efficiency are obtained for superthermal and subthermal electrons. By using a few adjustable parameters for intermediate energies, an accurate formula for the efficiency is obtained by fitting numerical results. This includes trapping effects and is valid for all frequencies up to the lower hybrid range of frequencies. It is found that for low‐frequency fast‐wave current drive, the relativistic and nonrelativistic efficiencies agree to within 15% up to 500 keV, although the relativistic corrections to power absorption and current density can be much larger separately. Relativistic effects on the efficiency become prominent at lower energies for Landau damping.

A new, enhanced performance tokamak regime, the second stable core VH-mode (SSC-VH), with a self-consistent VH-mode transport barrier and a large second stable core pressure gradient supported by negative central magnetic shear, is proposed. The SSC-VH is shown to have promising $\ensuremath{\beta}$ limits simultaneously with enhanced confinement and a large, well-aligned bootstrap current fraction. Simulations show that a wall-stabilized high $\ensuremath{\beta}$, high-confinement SSC-VH can be maintained self-consistently in a steady state, by noninductive current drive.

A fully relativistic theory of electron cyclotron current drive (ECCD) efficiency based on Green’s function techniques is considered. Numerical calculations of the current drive efficiency in a uniform magnetic field are performed. The numerical results with parameter regimes relevant to ITER operation are compared with those of two simplified models in which the electronelectron Coulomb collision operator is respectively approximatedbyitshigh-velocitylimitandasemirelativistic form. Our results indicate that the semirelativistic approximation of the collision operator should be appropriate for modeling the ECCD efficiency under ITER conditions.

Current drive experiments have been performed on the DIII-D tokamak using fast waves, electron cyclotron waves, and neutral injection. Fast wave experiments were performed using a 4-strap antenna with 1 MW of power at 60 MHz. These experiments showed effective heating of electrons, with a global heating efficiency equivalent to that of neutral injection even when the single pass damping was calculated to be as small as 5%. The damping was probably due to the effect of multiple passes of the wave through the plasma. Fast wave current drive experiments were performed with a toroidally directional phasing of the antenna straps. Currents driven by fast wave current drive (FWCD) in the direction of the main plasma current of up to 100 kA were found, not including a calculated 40 kA of bootstrap current. Experiments with FWCD in the counter current direction showed little current drive. In both cases, changes in the sawtooth behavior and the internal inductance qualitatively support the measurement of FWCD. Experiments on electron cyclotron current drive have shown that 100 kA of current can be driven by 1 MW of power at 60 GHz. Calculation with a Fokker-Planck code show that electron cyclotron current drive (ECCD) can be well predicted when the effects of electron trapping and of the residual electric field are included.

A simple theory for the study of stability and beam energy scaling of laser wake field accelerators (LWFA) was derived on the basis of the balance between the ponderomotive force due to the laser pulse and the restoring force due to the background ions. The theoretical analysis shows that the curvature of the accelerating structure is proportional to the relativistic plasma wavelength, which determines the beam energy scaling of a stably operated LWFA. Two dimensional particle-in-cell simulations were performed that demonstrate the fluctuation of the maximum energy gain of an accelerated electron bunch due to the unstable accelerating structure, which length is dynamically oscillating between the plasma wavelength and the relativistic plasma wavelength within a range of the laser intensity. The unstable accelerating structure can be stabilized by varying the laser intensity or reducing the plasma density. The simulation results reveal the existence of the parameter space for stable operations of a LWFA. The comparisons between the energy scaling law derived by the simple theory, the numerical results, and previous experimental results with self-guided laser pulses show good agreement and prove the simple theory can provide a good estimation of the beam energy for designing a new LWFA experiment.

We present a new technique to generate a high‐power pulse burst with a repetition rate of greater than 107 pulses per second. The circuit consists of transmission lines segmented by saturable inductors or ferrite‐filled coaxial cables in which an electromagnetic shock wave is driven. Small scale experiments have demonstrated that a burst of ten pulses can be easily generated.

The wave reflection and transmission in a nonlinear LC transmission line terminated with a resistive load are studied numerically. It is found that the soliton signals in the strongly nonlinear transmission line are almost perfectly absorbed by the linear resistor terminating the transmission line.

The thermal relaxation time of a one-dimensional plasma has been demonstrated to scale with ND2 due to discrete particle effects by collisionless particle-in-cell (PIC) simulations, where ND is the particle number in a Debye length. The ND2 scaling is consistent with the theoretical analysis based on the Balescu-Lenard-Landau kinetic equation. However, it was found that the thermal relaxation time is anomalously shortened to scale with ND while externally introducing the Krook type collision model in the one-dimensional electrostatic PIC simulation. In order to understand the discrete particle effects enhanced by the Krook type collision model, the superposition principle of dressed test particles was applied to derive the modified Balescu-Lenard-Landau kinetic equation. The theoretical results are shown to be in good agreement with the simulation results when the collisional effects dominate the plasma system.

In the limit that the electron thermal velocity greatly exceeds the fast ion velocity for electrical currents driven by neutral beams, the trapped electron correction to the Ohkawa current and the electron density gradient contribution to bootstrap current are shown to share the same transport coefficient in the banana regime. Therefore, existing analytic expressions for the bootstrap coefficient valid for arbitrary aspect ratio tokamaks can also be used to calculate the trapped electron effect.

An upper bound and a lower bound of the effective trapped particle fraction, ft, 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 ft over a wide range of equilibrium parameters.

A271 ELECTRON CYCLOTRON CURRENT DRIVE IN DIII-D: EXPERIMENT AND THEORY. Experiments on the DIII-D tokamak in which the measured off-axis electron cyclotron current drive has been compared systematically to theory over a broad range of parameters have shown that the Fokker-Planck code CQL3D provides an excellent model of the relevant current drive physics. This physics understanding has been critical in optimizing the application of ECCD to high performance discharges, supporting such applications as suppression of neoclassical tearing modes and control and sustainment of the current profile.

ARIES-ST, a fusion power plant design based on the spherical tokamak concept, has many attractive features, including high beta and power density, low magnetic field, high self-driven current, and a compact power core. The physics basis for three aspects of the plasma performance and operation, namely, MHD stability, current drive and profile control, and startup have been investigated during the first phase of the design, and the results to date are reported.

Numerical thermalization in collisional one-dimensional (1D) electrostatic (ES) particle-in-cell (PIC) simulations was investigated. Two collision models, the pitch-angle scattering of electrons by the stationary ion background and large-angle collisions between the electrons and the neutral background, were included in the PIC simulation using Monte-Carlo methods. The numerical results show that the thermalization times in both models were considerably reduced by the additional Monte-Carlo collisions as demonstrated by comparisons with Turner's previous simulation results based on a head-on collision model [M. M. Turner, Phys. Plasmas 13, 033506 (2006)]. However, the breakdown of Dawson's scaling law in the collisional 1D ES PIC simulation is more complicated than that was observed by Turner, and the revised scaling law of the numerical thermalization time with numerical parameters are derived on the basis of the simulation results obtained in this study.

A local representation is used to determine localized features in the current profiles due to ECCD in the DIII-D tokamak discharges from equilibrium reconstruction based on spectroscopic and external magnetic measurements. Initial results indicate that reconstruction using a local basis function can resolve very peaked ECCD profiles. The reconstructed narrow ECCD profiles are consistent with the quasi-linear Fokker-Planck results from the CQL3D code.

Lorentz gas model is used to examine collisionality modification of the trapped electron effects on electron cyclotron current drive efficiency. Appreciable collisionality enhancement of the current drive efficiency appears to be possible in the strong trapping cases in present-day current drive experiments.

Increased efficiency of off-axis electron cyclotron current drive (ECCD) has been obtained in discharges in DIII-D with higher electron beta, and these results have been understood by studying computationally the particle fluxes in velocity space driven by the EC waves. The relativistic cyclotron resonance tends to shift away in velocity space from the trapped-passing boundary for low-field-side launch as the electron temperature and/or density rise, increasing the net efficiency toward that of the trapping-free Fisch-Boozer level. Calculations with the CQL3D Fokker-Planck code illustrate clearly that the flux in velocity space due to rf-induced diffusion moves away from the trapping boundary for values of βe which have been realized in the experiments.

Electron cyclotron current drive (ECCD) experiments on the DIII-D tokamak are solidifying the physics basis for localized, off-axis current drive in both standard and advanced operating modes, the goal being to validate a predictive model for ECCD. The measured ECCD efficiency is found to be in agreement with theoretical calculations using the CQL3D Fokker-Planck code over a range of toroidal injection angles, absorption radii, and electron beta. The latter dependence is especially important since the ECCD efficiency is shown to increase with local electron beta, which is favorable for current profile control using off-axis ECCD in high-beta advanced tokamaks.

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 Euler equations are obtained exactly in the limit of zero time step. Using this equilibrium distribution function, we show that our algorithm has inherent positive hyperviscosity and hyperdiffusivity, for very small values of viscosity and thermal diffusivity, which are lacking in the standard algorithm. Short-wavelength modes are shown to be stable for temperatures greater than a lower limit. Results from a computer code are used to compare these algorithms, and to confirm the damping rate predictions made analytically. Finite amplitude sound waves in the simulated fluid steepen, as expected from gas dynamic theory.

Advanced tokamaks seek to achieve a high bootstrap current fraction without sacrificing fusion power density or fusion gain. Good progress has been made towards the DIII-D research goal of demonstrating a high-β advanced tokamak plasma in steady state with a relaxed, fully non-inductive current profile and a bootstrap current fraction greater than 50%. The limiting factors for transport, stability, and current profile control in advanced operating modes are discussed in this paper.

Clear measurements of the localized current density driven by electron cyclotron waves have been made on the DIII-D tokamak. Direct evidence of the current drive is seen on the internal magnetic field measurements by motional Stark effect spectroscopy. Comparison with theoretical calculations in the collisionless limit shows the experimental current drive exceeds the predictions by a substantial amount for currents driven near the half radius. In all cases the experimental current density profile is broader than the predicted one.

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.