Pedestal Model Research Articles

Pedestal study across a deuterium fuelling scan for high δ ELMy H-mode plasmas on JET with the carbon wall

We present the results from a new fuelling scan database consisting of 14 high triangularity (δ ∼ 0.41), type I ELMy H-mode JET plasmas. As the fuelling level is increased from low, (ΓD ∼ 0.2 × 1022 el s−1, ne,ped/nGW = 0.7), to high dosing (ΓD ∼ 2.6 × 1022 el s−1, ne,ped/nGW = 1.0) the variation in ELM behaviour is consistent with a transition from ‘pure type I’ to ‘mixed type I/II’ ELMs (Saibene et al 2002 Plasma Phys. Control. Fusion 44 1769). However, the pulses in this new database are better diagnosed in comparison to previous studies and most notable have pedestal measurements provided by the JET high resolution Thomson scattering (HRTS) system. We continue by presenting, for the first time, the role of pedestal structure, as quantified by a least squares mtanh fit to the HRTS profiles, on the performance across the fuelling scan. A key result is that the pedestal width narrows and peak pressure gradient increases during the ELM cycle for low fuelling plasmas, whereas at high fuelling the pedestal width and peak pressure gradient saturates towards the latter half of the ELM cycle. An ideal MHD stability analysis shows that both low and high fuelling plasmas move from stable to unstable approaching the ideal ballooning limit of the finite peeling–ballooning stability boundary. Comparison to EPED predictions show on average good agreement with experimental measurements for both pedestal height and width however when presented as a function of pedestal density, experiment and model show opposing trends. The measured pre-ELM pressure pedestal height increases by ∼20% whereas EPED predicts a decrease of 25% from low to high fuelling. Similarly the measured pressure pedestal width widens by ∼55%, in poloidal flux space, whereas EPED predicts a decrease of 20% from low to high fuelling. We give two possible explanations for the disagreement. First, it may be that EPED under predicts the critical density, which marks the transition from kink-peeling to ballooning-limited plasmas. Second, the stronger broadening of the experimental pedestal width than predicted by EPED is an indication that other transport related processes contribute to defining the pedestal width such as enhanced inter-ELM transport as observed at high fuelling, for mixed type I/II ELMy pulses.

Pedestal structure and stability in H-mode and I-mode: a comparative study on Alcator C-Mod

New experimental data from the Alcator C-Mod tokamak are used to benchmark predictive modelling of the edge pedestal in various high-confinement regimes, contributing to greater confidence in projection of pedestal height and width in ITER and reactors. ELMy H-modes operate near stability limits for ideal peeling–ballooning modes, as shown by calculations with the ELITE code. Experimental pedestal width in ELMy H-mode scales as the square root of βpol at the pedestal top, i.e. the dependence expected from theory if kinetic ballooning modes (KBMs) were responsible for limiting the pedestal width. A search for KBMs in experiment has revealed a short-wavelength electromagnetic fluctuation in the pedestal that is a candidate driver for inter-edge localized mode (ELM) pedestal regulation. A predictive pedestal model (EPED) has been tested on an extended set of ELMy H-modes from C-Mod, reproducing pedestal height and width reasonably well across the data set, and extending the tested range of EPED to the highest absolute pressures available on any existing tokamak and to within a factor of three of the pedestal pressure targeted for ITER. In addition, C-Mod offers access to two regimes, enhanced D-alpha (EDA) H-mode and I-mode, that have high pedestals, but in which large ELM activity is naturally suppressed and, instead, particle and impurity transport are regulated continuously. Pedestals of EDA H-mode and I-mode discharges are found to be ideal magnetohydrodynamic (MHD) stable with ELITE, consistent with the general absence of ELM activity. Invocation of alternative physics mechanisms may be required to make EPED-like predictions of pedestals in these kinds of intrinsically ELM-suppressed regimes, which would be very beneficial to operation in burning plasma devices.

Simulations of ITER in the presence of ITB using the NTV intrinsic toroidal rotation model

Simulations of a standard H-mode International Thermonuclear Experimental Reactor (ITER) scenario in the presence of internal transport barrier (ITB) are carried out using the 1.5D BALDUR integrated predictive modelling code. The intrinsic offset toroidal rotation, which can play an essential role in turbulent transport suppression that results in the ITB formation, is theoretically calculated using a model based on the neoclassical toroidal viscosity (NTV) concept. The core transport in this simulation is a combination of a mixed Bohm/gyro-Bohm anomalous transport model and an NCLASS neoclassical transport model. The boundary condition of the simulations is taken to be at the top of the pedestal where the pedestal value is calculated using the pedestal model based on a combination of pedestal width scaling determined by magnetic/flow shear stabilization and an infinite-n ballooning pressure gradient model. It is found that the predicted intrinsic rotation can result in the formation of ITB, locating mostly between r/a = 0.6 and 0.8 and having a strong impact on the plasma performance in ITER. It is also found that the variations of plasma density and heating power result in a minimal change in toroidal rotation; whereas the increase in plasma effective charge can considerably reduce the toroidal velocity peaking.

Comparisons of paleoclassical based pedestal model predictions of electron quantities to measured DIII-D H-mode profiles

Accurately predicting the pedestal structure in high-(H-)confinement mode plasmas is of great importance for the modelling of future tokamak plasmas. The main predictions of a model of pedestal structure based on paleoclassical transport as the main transport mechanism are presented. Numerical evaluations of this model are compared with a database of measured DIII-D H-mode pedestal profiles. Across the database, the electron temperature gradient is overpredicted by a factor of 1.7 ± 1.1 and the electron density by a factor of 2.1 ± 0.7. These results are consistent with paleoclassical transport producing the minimum level of electron transport. Trends in the predictions indicate that some additional transport may be operative, especially in high βp and low confinement plasmas.

Optimized Multigrid Strategy for Accurate Flare Modeling with Three-Dimensional Mask Effect in Extreme-Ultraviolet Lithography

Extreme-ultraviolet (EUV) lithography has many critical challenges regarding its implementation in the semiconductor industry. One of the main challenges is flare, the unwanted total integrated light scattering at the wafer level, which reduces the critical dimension and imaging performance. Therefore, EUV flare has been intensively studied and has been compensated by a rule-based method for many years. However, there are few results with regard to developing more accurate and feasible flare-modeling techniques to enable us to satisfy the criteria of the sub-22 nm half pitch (HP) technology node and beyond. In this work, we studied an improved flare-modeling technique considering the interaction of scattered EUV light with a three-dimensional EUV mask topography in order to obtain an accurate flare distribution and an optimized multigrid strategy for generating a flare map over the full-field scale. Also, we proposed a flare-modeling technique based on the pedestal model, which we developed using novel effective reflection coefficients in order to achieve sufficient accuracy. Such an approach is thought to be needed instead of the conventional pattern density approach in preparation for upcoming advanced HP technology nodes or for different absorber materials and illumination angles. Lastly, the need for a flare map shift to compensate for the mask defocus error is introduced and some flare evaluations of mask patterns used in the exposure-dose-monitoring technique were performed.

The EPED pedestal model and edge localized mode-suppressed regimes: Studies of quiescent H-mode and development of a model for edge localized mode suppression via resonant magnetic perturbations

The EPED model predicts the H-mode pedestal height and width based upon two fundamental and calculable constraints: (1) onset of non-local peeling-ballooning modes at low to intermediate mode number, (2) onset of nearly local kinetic ballooning modes at high mode number. We present detailed tests of the EPED model in discharges with edge localized modes (ELMs), employing new high resolution measurements, and finding good quantitative agreement across a range of parameters. The EPED model is then applied for the first time to quiescent H-mode (QH), finding a similar level of agreement between predicted and observed pedestal height and width, and suggesting that the model can be used to predict the critical density for QH-mode operation. Finally, the model is applied toward understanding the suppression of ELMs with 3D resonant magnetic perturbations (RMP). Combining EPED with plasma response physics, a new working model for RMP ELM suppression is developed. We propose that ELMs are suppressed when a “wall” associated with the RMP blocks the inward penetration of the edge transport barrier. A calculation of the required location of this “wall” with EPED is consistent with observed profile changes during RMP ELM suppression and offers an explanation for the observed dependence on safety factor (q95).

H-mode pedestal scaling in DIII-D, ASDEX Upgrade, and JET

Multi device pedestal scaling experiments in the DIII-D, ASDEX Upgrade (AUG) and JET tokamaks are presented in order to test two plasma physics pedestal width models. The first model proposes a scaling of the pedestal width Δ/a ρ * 1/2 to ρ * based on the radial extent of the pedestal being set by the point where the linear turbulence growth rate exceeds the ExB velocity. In the multi device experiment where ρ * at the pedestal top was varied by a factor of four while other dimensionless parameters where kept fixed, it has been observed that the temperature pedestal width in real space coordinates scales with machine size, and that therefore the gyroradius scaling suggested by the model is not supported by the experiments. This density pedestal width is not invariant with ρ * which after comparison with a simple neutral fuelling model may be attributed to variations in the neutral fuelling patterns. The second model, EPED1, is based on kinetic ballooning modes setting the limit of the radial extent of the pedestal region and leads to Δ βp 1/2 . All three devices show a scaling of the pedestal width in normalised poloidal flux as Δ βp 1/2 , as described by the kinetic ballooning model, however on JET and AUG this could not be distinguished from an interpretation where the pedestal is fixed in real space. Pedestal data from all three devices have been compared with the predictive pedestal model EPED1 and the model produces pedestal height values that match the experimental data well.

Pellet injection into H-mode ITER plasma with the presence of internal transport barriers

The impacts of pellet injection into ITER type-1 ELMy H-mode plasma with the presence of internal transport barriers (ITBs) are investigated using self-consistent core-edge simulations of 1.5D BALDUR integrated predictive modeling code. In these simulations, the plasma core transport is predicted using a combination of a semi-empirical Mixed B/gB anomalous transport model, which can self-consistently predict the formation of ITBs, and the NCLASS neoclassical model. For simplicity, it is assumed that toroidal velocity for ωE×B calculation is proportional to local ion temperature. In addition, the boundary conditions are predicted using the pedestal temperature model based on magnetic and flow shear stabilization width scaling; while the density of each plasma species, including both hydrogenic and impurity species, at the boundary are assumed to be a large fraction of its line averaged density. For the pellet’s behaviors in the hot plasma, the Neutral Gas Shielding (NGS) model by Milora-Foster is used. It was found that the injection of pellet could result in further improvement of fusion performance from that of the formation of ITB. However, the impact of pellet injection is quite complicated. It is also found that the pellets cannot penetrate into a deep core of the plasma. The injection of the pellet results in a formation of density peak in the region close to the plasma edge. The injection of pellet can result in an improved nuclear fusion performance depending on the properties of pellet (i.e., increase up to 5% with a speed of 1 km/s and radius of 2 mm). A sensitivity analysis is carried out to determine the impact of pellet parameters, which are: the pellet radius, the pellet velocity, and the frequency of injection. The increase in the pellet radius and frequency were found to greatly improve the performance and effectiveness of fuelling. However, changing the velocity is observed to exert small impact.

An acoustic-structural model for pedestal-radiated noise during ball bearing angular acceleration

The purpose of this paper is to numerically investigate the noise characteristics of a pedestal during rolling element bearing angular acceleration while under radial load. A dynamic model was built for the calculation of excitation of the pedestal during angular acceleration, taking account of contact forces and friction forces between rolling elements and the races and skidding of rolling elements. The displacement of the outer race obtained from the dynamic model was then used in the pedestal finite element model and the vibration of the pedestal was obtained by performing transient dynamic analysis using ANSYS. The structural vibration acceleration of the pedestal was used as a boundary condition for the pedestal boundary element model and the sound pressure level was computed using LMS-SYSNOISE. Finally, the pedestal-radiated noise characteristics and how much the pedestal-radiated noise can be affected by design parameters, such as friction coefficient and radial load, was investigated. The proposed model and the results of the present paper could aid in the design of low-noise rolling element bearings and help solve the noise problem related to such bearings.

Impacts of pellets injected from the low-field side on plasma in ITER

Impacts of pellets injected from the low-field side (LFS) on plasma in ITER are investigated using the 1.5D BALDUR integrated predictive modeling code. In these simulations, the pellet ablation is described using the neutral gas shielding (NGS) model. The pellet ablation model is coupled with the plasma core transport model, which is a combination of the MMM95 anomalous transport model and NCLASS neoclassical transport model. The boundary conditions are assumed to be at the top of the pedestal, in which the pedestal parameters are predicted using a pedestal model based on the theoretical-based pedestal width scaling (either magnetic and flow shear stabilization width scaling, or flow shear stabilization width scaling, or normalized poloidal pressure width scaling) and the infinite-n ballooning mode pressure gradient limit. These pedestal models depend sensitively on the density at the top of the pedestal, which can be strongly influenced by the injection of pellets. The combination of the MMM95 and NCLASS models, together with the pedestal and NGS models, is used to simulate the time evolution of the plasma current, ion and electron temperatures, and density profiles for ITER standard type-I ELMy H-mode discharges during the injection of LFS pellets. It is found that the injection of pellets results in a complicated plasma scenario, especially in the outer region of the plasma and the plasma conditions at the boundary in which the pellet has an impact on increasing the plasma edge density, but reducing the plasma edge temperature. The LFS pellet has a stronger impact on the edge as compared to the center. For fusion performance, the pellet can result in either enhancement or degradation, depending sensitively on the pellet parameters; such as the pellet size, pellet velocity, and pellet frequency. For example, when a series of deuterium pellets with a size of 0.5 cm, velocity of 1 km/s, and frequency of 2 Hz are injected into the ITER plasma from the LFS, the plasma performance, evaluated in terms of Q fusion, can increase to 72% of that before the use of pellets. It is also found that the injection of pellets results in an increase in the ion and electron densities, but does not enhance the central plasma density. On the other hand, it results in the formation of another peak of the plasma density in the outer region near the plasma edge. The formation of the density peak results in the reduction of plasma transports near the edge by decreasing the contributions of ion-temperature-gradient and trapped electron modes, as well as kinetic ballooning modes.

Model for toroidal velocity in H-mode plasmas in the presence of internal transport barriers

A model for predicting toroidal velocity in H-mode plasmas in the presence of internal transport barriers (ITBs) is developed using an empirical approach. In this model, it is assumed that the toroidal velocity is directly proportional to the local ion temperature. This model is implemented in the BALDUR integrated predictive modelling code so that simulations of ITB plasmas can be carried out self-consistently. In these simulations, a combination of a semi-empirical mixed Bohm/gyro-Bohm (mixed B/gB) core transport model that includes ITB effects and NCLASS neoclassical transport is used to compute a core transport. The boundary is taken to be at the top of the pedestal, where the pedestal values are described using a theory-based pedestal model based on a combination of magnetic and flow shear stabilization pedestal width scaling and an infinite-n ballooning pressure gradient model. The combination of the mixed B/gB core transport model with ITB effects, together with the pedestal and the toroidal velocity models, is used to simulate the time evolution of plasma current, temperature and density profiles of 10 JET optimized shear discharges. It is found that the simulations can reproduce an ITB formation in these discharges. Statistical analyses including root mean square error (RMSE) and offset are used to quantify the agreement. It is found that the averaged RMSE and offset among these discharges are about 24.59% and −0.14%, respectively.

Progress towards a predictive model for pedestal height in DIII-D

Recent DIII-D pedestal studies provide improved characterization of pedestal scaling for comparison with models. A new pedestal model accurately predicts the maximum achieved pedestal width and height in type I ELMing discharges over a large range of DIII-D operational space, including ITER demonstration discharges. The model is a combination of the peeling–ballooning theory for the MHD stability limits on the pedestal with a simple pedestal width scaling in which the width is proportional to the square root of the pedestal poloidal beta. Width scalings based on the ion toroidal or poloidal gyroradius are much poorer descriptions of DIII-D data. A mass scaling experiment in H and D provides support for a poloidal beta scaling and is not consistent with an ion poloidal gyroradius scaling. Studies of pedestal evolution during the inter-ELM cycle provide evidence that both the pedestal width and height increase during pedestal buildup. Model studies with a 1D kinetic neutrals calculation show that the temporal increase in density width cannot be explained in terms of increased neutral penetration depth. These studies show a correlation of pedestal width with both the square root of the pedestal poloidal beta and the square root of the pedestal ion temperature during the pedestal buildup.

Simulations of ITER with combined effects of internal and edge transport barriers

Predictive simulations of ITER with the presence of both an edge transport barrier (ETB) and an internal transport barrier (ITB) are carried out using the BALDUR integrated predictive modelling code. In these simulations, the boundary is taken at the top of the pedestal, where the pedestal values are described using theory-based pedestal models. These pedestal temperature models are based on three different pedestal width scalings: magnetic and flow shear stabilization (Δ ∝ ρis2), flow shear stabilization () and normalized poloidal pressure (). The pedestal width scalings are combined with a pedestal pressure gradient scaling based on the ballooning mode limit to predict the pedestal temperature. A version of the semi-empirical Mixed Bohm/gyroBohm (Mixed B/gB) core transport model that includes ITB effects is used to compute the evolution of plasma profiles. In this model, the anomalous transport in the core is stabilized by the influence of Er × B flow shear and magnetic shear, which results in the formation of ITB. The combination of the Mixed B/gB core transport model with ITB effects, together with the pedestal model, is used to simulate the time evolution of plasma current, temperature, and density profiles for ITER standard type I ELMy H-mode discharges. It is found that ITER fusion performance using the BALDUR code with Mixed B/gB transport model without the presence of ITB is quite pessimistic (Fusion Q ∼ 3). The presence of ITB is crucial and can result in a significant improvement, which is needed for achieving a target Fusion Q of 10. The improvement due to the presence of ITB is almost the same for all simulations with those three pedestal temperature models. This is caused by the predicted pedestal temperature from each pedestal temperature model varying just slightly. The presence of ITB has a strong impact on both temperature profiles, especially near the centre of the plasma, but has a small impact on electron, deuterium, tritium and carbon density profiles, except the helium density profile. The formation of ITB does not impact on the pedestal. It is also found that during a sawtooth crash, the temperature profiles drop significantly, but there is a small change in the density profiles. However, the sawtooth oscillation has no impact on the pedestal. When the auxiliary heating power is turned off, it is found that significant fusion power is sustained.

A pedestal temperature model with self-consistent calculation of safety factor and magnetic shear

A pedestal model based on theory-motivated models for the pedestal width and the pedestal pressure gradient is developed for the temperature at the top of the H-mode pedestal. The pedestal width model based on magnetic shear and flow shear stabilization is used in this study, where the pedestal pressure gradient is assumed to be limited by first stability of infinite n ballooning mode instability. This pedestal model is implemented in the 1.5D BALDUR integrated predictive modeling code, where the safety factor and magnetic shear are solved self-consistently in both core and pedestal regions. With the self-consistently approach for calculating safety factor and magnetic shear, the effect of bootstrap current can be correctly included in the pedestal model. The pedestal model is used to provide the boundary conditions in the simulations and the Multi-mode core transport model is used to describe the core transport. This new integrated modeling procedure of the BALDUR code is used to predict the temperature and density profiles of 26 H-mode discharges. Simulations are carried out for 13 discharges in the Joint European Torus and 13 discharges in the DIII-D tokamak. The average root-mean-square deviation between experimental data and the predicted profiles of the temperature and the density, normalized by their central values, is found to be about 14%.

Integrated Simulation Code for Burning Plasma Analysis

A strategy for integrated modeling of burning plasmas at Japan Atomic Energy Agency is described. In order to simulate the burning plasma, which has the complex feature of widely different timescales and spatial scales, a simulation code cluster based on the TOPICS transport code is being developed by integrating heating and current drive, impurity transport, the edge pedestal model, the divertor model, the magnetohydrodynamics (MHD), and the high-energy behavior model. The developed integration models are validated by fundamental research from JT-60U experiments and the simulation based on the First Principle in our strategy. The integration of MHD stability and the transport progresses for three phenomena with different timescales of neoclassical tearing modes (NTMs) (~τNTM ~ 10-2τR), beta limits (~τAlfvén), and edge-localized modes (ELMs) (intermittent of τE and τAlfvén). Here, τR, τAlfvén, and τE are the resistive skin time, the Alfvén transit time, and the energy confinement time, respectively. The integrated model of the NTM is produced by coupling the modified Rutherford equation with the transport equation. The integrated model of the beta limits is developed by the low-n stability analysis of downstreaming data from the TOPICS code. The integrated model of the ELM is developed by the iterative calculation of the MARG2D ideal MHD stability code and the TOPICS code. These models are being validated by the data from the JT-60 experiments and estimate the plasma performance for burning plasmas.

Effect of isotope mass on simulations of the high-mode pedestal and edge localized modes

Simulations of Joint European Torus (JET) [P. H. Rebut et al., Nucl. Fusion 25, 1011 (1985)] type I high-mode (H-mode) discharges with edge localized modes (ELMs) are used to study the effect of isotope mass on the height of the pedestal and the frequency of ELMs. A dynamic model for the H-mode pedestal and ELM cycles is employed in the JETTO integrated modeling code [M. Erba et al., Plasma Phys. Control. Fusion 39, 261 (1997)]. The stability criteria that are used to trigger ELM crashes in the JETTO simulations are calibrated with the HELENA and MISHKA ideal magnetohydrodynamic (MHD) stability codes [A. B. Mikhailovskii et al., Plasma Phys. Rep. 23, 713 (1997)]. Results obtained using a pedestal model in which the pedestal width increases with isotope mass are compared with those obtained using a fixed, prescribed pedestal width. In JET type I ELMy H-mode discharges, it is found that the height of the pressure pedestal increases and that the frequency of the ELMs decreases as the isotope mass is increased. Both of these experimentally observed trends are obtained simultaneously in the simulations only if the pedestal width increases with isotope mass. The physical processes that play a significant role in these simulations are described.

Integrated pedestal and core modeling of Joint European Torus (JET) triangularity scan discharges

Simulations of four Joint European Torus (JET) [Rebut et al., Nucl. Fusion 25, 1011 (1985)] type I ELMy high confinement mode discharges in a triangularity scan are carried out using the JETTO integrated modeling code [Erba et al., Plasma Phys. Contolled Fusion 39, 261 (1997)] with a predictive core transport model and a pedestal model that includes the effects of edge localized modes (ELMs). The pedestal pressure gradient is limited by the magnetohydrodynamic (MHD) ballooning mode instability, which triggers ELM crashes in these simulations. The validation of the pressure gradient limit used in the simulations is confirmed by a stability analysis carried out using the HELENA and MISHKA codes [Mikhailovskii et al., Plasma Phys. Rep 23, 713 (1997)]. The MHD stability analysis includes infinite-n ideal ballooning, finite-n ballooning, and low-n kink/peeling modes. It is shown that higher triangularity plasmas have easier access to the second stability region, which allows the edge pressure gradients in the higher triangularity discharges to increase to higher levels.

Integrated predictive modeling of high-mode tokamak plasmas using a combination of core and pedestal models

A new integrated modeling protocol is developed using a model for the temperature and density pedestal at the edge of high-mode (H-mode) plasmas [Onjun et al., Phys. Plasmas 9, 5018 (2002)] together with the Multi-Mode core transport model (MMM95) [Bateman et al., Phys. Plasmas 5, 1793 (1998)] in the BALDUR integrated modeling code to predict the temperature and density profiles of 33 H-mode discharges. The pedestal model is used to provide the boundary conditions in the simulations, once the heating power rises above the H-mode power threshold. Simulations are carried out for 20 discharges in the Joint European Torus and 13 discharges in the DIII-D tokamak. These discharges include systematic scans in normalized gyroradius, plasma pressure, collisionality, isotope mass, elongation, heating power, and plasma density. The average rms deviation between experimental data and the predicted profiles of temperature and density, normalized by central values, is found to be about 10%. It is found that the simulations tend to overpredict the temperature profiles in discharges with low heating power per plasma particle and to underpredict the temperature profiles in discharges with high heating power per particle. Variations of the pedestal model are used to test the sensitivity of the simulation results.

Integrated predictive modelling simulations of burning plasma experiment designs

Models for the height of the pedestal at the edge of H-mode plasmas (Onjun T et al 2002 Phys. Plasmas 9 5018) are used together with the Multi-Mode core transport model (Bateman G et al 1998 Phys. Plasmas 5 1793) in the BALDUR integrated predictive modelling code to predict the performance of the ITER (Aymar A et al 2002 Plasma Phys. Control. Fusion 44 519), FIRE (Meade D M et al 2001 Fusion Technol. 39 336), and IGNITOR (Coppi B et al 2001 Nucl. Fusion 41 1253) fusion reactor designs. The simulation protocol used in this paper is tested by comparing predicted temperature and density profiles against experimental data from 33 H-mode discharges in the JET (Rebut P H et al 1985 Nucl. Fusion 25 1011) and DIII-D (Luxon J L et al 1985 Fusion Technol. 8 441) tokamaks. The sensitivities of the predictions are evaluated for the burning plasma experimental designs by using variations of the pedestal temperature model that are one standard deviation above and below the standard model. Simulations of the fusion reactor designs are carried out for scans in which the plasma density and auxiliary heating power are varied.

Nonlinear Dynamic Analysis of a Rotor Shaft System With Viscoelastically Supported Bearings

This research investigates the dynamic analysis of a single-rotor shaft system with nonlinear elastic bearings at the ends mounted on viscoelastic suspension. Timoshenko shaft model is utilized to incorporate the flexibility of the shaft; the rotor is considered to be rigid and located at the mid-span of the shaft. A nonlinear bearing pedestal model is assumed which has a cubic nonlinear spring and linear damping characteristics. The viscoelastic supports are modeled using Kelvin-Voigt model. Free and forced vibration is investigated based on the direct multiple scales method of one-to-one frequency-to-amplitude relationship using third order perturbation expansion. The results of the nonlinear analysis show that a limiting value of the internal damping coefficient of the shaft exists where the trend of the frequency-response curve switches. Also, the primary resonance peak shifts to higher frequencies with the increase of the bearing nonlinear elastic characteristics, but with a flattened curve and hence lower peak values. A jump phenomenon takes place for high values of the bearing nonlinear elastic characteristics.