Fusion power production in ITER baseline H-mode scenarios T. Rafiq 1, A.H. Kritz 1, C.E. Kessel 2, and A.Y. Pankin 3

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1 Fusion power production in ITER baseline H-mode scenarios T. Rafiq 1, A.H. Kritz 1, C.E. Kessel 2, and A.Y. Pankin 3 1 Department of Physics, Lehigh University, Bethlehem, PA Princeton Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 854 and 3 Tech-X Corporation, Boulder, CO 833 (Dated: 1 April 215) Self-consistent simulations of 15 MA ITER H-mode DT scenarios, from ramp-up through flat-top, are carried out. Electron and ion temperatures, toroidal angular frequency and currents are evolved, in simulations carried out using the predictive TRANSPort and integrated modeling code (PTRANSP) code starting with initial profiles and equilibria obtained from tokamak simulation code (TSC) studies. Studies are carried out examining the dependence and sensitivity of fusion power production on electron density, argon impurity concentration, choice of radio frequency heating, pedestal temperature without and with E B flow shear effects included, and the degree of plasma rotation. The goal of these whole-device ITER simulations is to identify dependencies that might impact ITER fusion performance. I. INTRODUCTION Previous studies of ITER steady state and hybrid scenarios 1 3 are extended to studies of ITER 15 MA H- mode DT scenarios 4. Results are obtained using the predictive TRANSPort and integrated modeling code (PTRANSP) with time evolved boundary conditions and the plasma shape provided by the Tokamak Simulation Code (TSC) 1,5. The Multi-Mode anomalous transport model (MMM7.1) 6,7, combined with neoclassical transport, is utilized in the PTRANSP code to compute temperature, magnetic q and toroidal rotation profiles. The MMM7.1 module can be utilized to compute anomalous thermal, particle and momentum transport from the top of the pedestal to the magnetic axis for the H-mode discharges and from the plasma edge to the magnetic axis for the L-mode discharges. In addition, the Multi-Mode anomalous transport model is computationally efficient for use in carrying out whole-device modeling studies. The plasma parameters used in the simulations are: Major radius, 6.2 m; plasma radius, 2. m; axial magnetic field, 5.3 T; elongation, 1.8; and triangularity,.4. The plasma current in the simulations is ramped to 15 MA during first 1 sec and the central density is ramped to values in the range of m 3 to m 3. Variation in density and in level of Argon impurity provides insight to the sensitivity of fusion power production to variation in these parameters. The impurity concentrations considered are 2% Beryllium; 2% Helium-3 and Argon in the range.12% to.3%. In the simulations helium ash accumulates. Pedestal temperature is varied in the range 3. to 5. kev in order to examine the sensitivity of fusion power production to the pedestal temperature. The fusion power production is computed with the E B flow shear both off and on for pedestal temperatures of 3. kev, 4. kev and 5. kev. Simulations are carried out turning flow shear off in order to separate the flow shear and magnetic shear effects on internal transport barriers. This is an important issue for ITER since it is expected that the toroidal rotation in ITER will be small. The dependence of fusion power production on the effect of E B flow shear is also explored by varying the flow shear coefficient α (.,.5,.75 and 1.). In these simulations the same toroidal rotation frequency boundary condition, 3 krad/s at ρ =.8, is employed for each discharge. Components of the ITER H-mode plasma current density (ohmic, bootstrap, beam and radio frequency) are plotted as functions of plasma radius along with the integrated current contained within a given plasma radius. The neutron density production as a function of radius and the fusion power as a function of time is shown for the various scenario studies that have been carried out. In Sec. II below, the simulation protocol is described along with brief descriptions of the Multi-Mode anomalous transport model and the modules used for computing heating, current drive, and neoclassical transport. Simulation results are presented in Sec. III. These include the dependence of fusion power production on electron density, Argon concentration, choice of radio frequency heating, pedestal temperature, flow shear effects off as well as with flow shear effects on, and plasma rotation. The results are briefly summarized in Sec. IV. II. INTEGRATED MODELING SIMULATIONS The PTRANSP code builds on the capabilities that exist in the TRANSP analysis code. Advances in the PTRANSP code are focused on increasing the level of predictive capability for whole device modeling of existing and future machines. Thus, the PTRANSP code is an important tool in planning experimental campaigns. A number of theory based anomalous transport models have been introduced allowing for the study of the predicted evolution of temperature profiles, current profiles, and toroidal rotation. The transport model used in producing results presented in this paper is the MMM7.1 anomalous transport model 6,7. ITER simulations has also been carried out using GLF23 and an other anoma-

2 2 lous transport models The MMM7.1 transport model is a stiff transport model that is at a critical temperature gradient there is a rapid increase in thermal diffusivity. Solvers have been advanced in the PTRANSP code in order to produce numerically stable predictions when the stiff anomalous transport models are used to predict the level of anomalous transport. The MMM7.1 is used to predict the evolution of plasma temperature and toroidal angular frequency. Components of the Multi-Mode model include: The Weiland19 model 12 for the contributions to transport resulting from ITG/TEM/MHD drift modes; the Horton model 13 for the contribution that results from ETG mode turbulence; and the Rafiq Drift Resistive Inertial Ballooning Mode, the DRIBM model 14, for contributions associated with ballooning modes. The Weiland19 model is based on a fluid description of collective behavior of ITG/TEM/MHD modes. In addition to thermal transport, the MMM7.1 model is used to compute, ITG/TEM driven momentum diffusion and convection. The ETG transport includes a threshold obtained from toroidal gyrokinetic ETG turbulence simulations 15. The DRIBM component of MMM7.1 describes transport driven by gradients, inductive effects and electron inertia. The transport resulting from this mode is particularly sensitive to the resistivity, magnetic-q and gradients near the plasma edge. It is important to note that MMM7.1 is used with no adjustable parameters. The MMM7.1 anomalous transport model described above is combined with neoclassical ion thermal transport, typically provided by the NCLASS module, and can be combined with the Callen model for paleoclassical transport, which yields an irreducible level of electron heat transport and scales like the neoclassical electrical resistivity. However, it turns out that if the paleoclassical model is included in ITER simulations, its contribution to transport is negligible. The NCLASS module is also used to compute the neoclassical plasma resistivity, bootstrap current density and neoclassical poloidal rotation velocity. Auxiliary heating and current drive sources are computed in PTRANSP using the NTCC NUBEAM module 16,17 for neutral beam injection (NBI), the TORIC full wave module 18,19 for ion cyclotron resonance heating (ICRH), the TORAY module 2 for electron cyclotron resonance heating (ECRH), and the LSC 1-D ray-tracing quasilinear Fokker Planck module 21 for lower hybrid heating (LH). The NUBEAM module is used to compute neutral beam deposition, beam torque, as well as the slowing down, pitch angle scattering, and thermalization of beam ions and fusion ions. In the simulations results presented below, two 1 MeV neutral beams are used, each with 16.5 MW of power. One beam is steered on-axis and other is steered off-axis. The first beam is turned on at time t = 75 sec, and second beam is turned on at t = 1 sec. The number of Monte Carlo particles used here is 4 each for beam ions and alpha particles. The frequency in the ICRH TORIC full wave module is set equal to 48 MHz; the minority He 3 density is assumed to be n He 3/n e =.2; the toroidal wave number is set to 27; the number of radial and poloidal grid points are set to 128 and 256, respectively; and the phasing of the antena element is assumed to be (, π,, π). The 2 MW ICRH heating is turned on at time t = 8 sec and the TORIC heating package in each PTRANSP simulation is called once per second. TORAY 2 is a ray-tracing 1D Fokker Planck module used in PTRANSP simulations. Three antennae in the TORAY module are used for ECRH heating and current drive. The antennae are located at (R, Z) locations where R = 8.51 m. The poloidal launch angle is set to 9 and the frequency for each antenna is 17 GHz. The launcher heights, Z, are.1 m,.611 m, m and the corresponding azimuthal launch angles are set to 4, 38, The ECRH heating is turned on at time t = 8 sec and the toray heating package in PTRANSP simulation is called once per second. The computation of lower hybrid heating and current drive in non-circular axisymmetric plasmas in the presence of an electric field 23 is carried out in the PTRANSP code using the LSC module 21. Details of geometry, plasma profiles and circuit equations are taken into account. The two dimensional velocity space effects are approximated in a one-dimensional Fokker Planck treatment. Atomic physics cross sections for ionization, recombination and impurity radiation are computed using the Atomic Data and Analysis Structure (ADAS) module 24 in the PTRANSP code. Fusion reaction rates are computed using the National Transport Code Collaboration 25 (NTCC) PREACT module. The temperature and width of the ITER H-mode edge pedestal are computed using the PEDESTAL module 26. The scaling factor in the PEDESTAL module is adjusted in order to obtain the EPED1 code predicted temperature pedestal height for the ITER discharges. The PEDESTAL module includes the models for the L-H transition, pedestal density and pedestal temperature. In the simulations, an automated transition between L- to H mode is triggered when the total power exceeds the empirically determined power threshold 27. The pedestal width and temperature computed using the adjusted PEDESTAL module are imposed as edge boundary conditions after the transition to H-mode occurs. The temperature profiles between the top of the pedestal and the plasma edge are approximated as a descending straight line. The EPED1 code provides a prediction of the baseline pressure at the top of the pedestal for based on constraints of the peeling-ballooning ideal MHD mode and the onset of a local kinetic ballooning mode 28. Earlier ITER studies included ELMs and neoclassical tearing modes Since ELMs, disruptions, and fast ion wave and MHD interactions are not modeled in the PTRANSP code, descriptions of these phenomena are not included in the results presented below.

3 3 III. SIMULATION RESULTS Simulation results shown in Figs. 1 and 2 are obtained with the temperature at the top of the pedestal equal to to 5. kev (consistent with the EPED1 code prediction) during the H-mode phase of the discharge. The L-H transition is predicted to occur when the input power is 44 MW. In Fig. 1(a), the components of heating power deposited to the ions and electrons are plotted as a function of time. In this ITER H-mode simulation the ICRH heating power is 2 MW and the NBI heating power is 33 MW. At 1 sec, out of 2 MW of ICRH heating, 13 MW is deposited on the ions and 7 MW is deposited on the electrons; and out of 33 MW of NBI heating, 12.7 MW to deposited on the ions and 15.1 MW is deposited on the electrons. Fast ion fusion results in 3.3 MW heating of ions. Approximately 1.6 MW shine-through occurs when neutral beams are first turned on, while essentially no shine-through is observed after 14 sec of the discharge. Some of the beam heating power is consumed as a limiter loss. It is recognized that baseline H-mode discharge can only continue at 15 MA for about 45-5 sec before the available flux swing from the solenoid is consumed and the plasma current ramped down. However, the H-mode simulations described in this paper are carried out for 1 sec in order to observe the relaxed state. The sources of heating power, when plotted as a function of radius (not shown here), are distributed over the central region of the plasma. The volumes associated with the flux surfaces near the magnetic axis are small, so they receive relatively little power. Even though the power deposition profile usually decreases with plasma minor radius increasing away from the plasma center, the integrated power within increasingly larger annular differential radii increases with radius before decreasing in the outer regions of the plasma. The components of the total plasma current (ohmic, bootstrap, beam driven, and ICRH driven) are shown as a function of time in Fig.1(b). The discharge is simulated from the low current 4.6 MA start-up stage well into the 15 MA flat-top burn phase of the discharge at which begins at approximately 1 sec. At 1 sec, the contributions to the current are the current driven inductively, 9.44 MA, the bootstrap current, 3.6 MA, the current driven by the injected neutral beam power, 1.6 MA, and the current driven by the injected ICRH power,.17 MA. The remaining.73 MA of current is the sum of toroidal and Pfirsch-Schlüter and diamagnetic currents. The radial dependence of the plasma current density is plotted in Panel (c) of Fig. 1 and the total current within a given plasma radius is plotted in the Panel (d) of Fig. 1 at time t = 1 sec. The radial variable ρ is the normalized square root of toroidal flux. Results are shown for each of the sources that contribute to the plasma current. Ohmic, beam driven and ICRH current densities are larger near the plasma center, while the bootstrap current density is larger at the plasma edge. Note, a given current density near the plasma center contributes less to the total current than the same current density nearer the plasma boundary, where differential cross-sectional area elements are larger. In Fig. 7, the fusion neutron density production as a function of radius and accumulation within a given radial location is illustrated for the ITER plasma with a pedestal temperature of 5. kev. It is seen that while the neutron density production is largest in the central region of the plasma where the temperature is highest, because of the volume effect, the rate of neutrons produced with in a given radius approaches its peak value midway between the center and edge of the plasma as shown in Panel b) of Fig. 2. Similar results for the fusion neutron density production as a function of radius and accumulation within a given radial location are found for ITER plasmas with pedestal temperatures 4. kev and 3. kev. In the following subsections various dependencies of fusion power production are examined. A. Sensitivity of Fusion Power to the Level of Electron Density In order to investigate the sensitivity of the fusion power production to the density level, simulations are carried out for discharges with a central electron density (in units of 1 2 ) of n e,2 =.91 m 3 and n e,2 = 1.5 m 3. The fusion power results obtained in simulations using the density profiles shown in Fig. 3a are indicated in Fig. 3b. In comparing the results obtained in the Low Density Case with those obtained in the High Density Case, it is seen that there is an increase in the fusion power from 6 MW (fusion Q=11.3) to 8 MW (fusion Q= 15.1). A comparable increase in fusion power is predicted in the simulations in which the GLF23 transport model is used. (The GLF23 results are not presented here.) B. Influence of Argon concentration on Fusion Power and on Radiated Power Simulations are carried out in order to investigate the decrease in fusion power and increase in radiated power that would occur if the central argon impurity density is increased from.14% of the central electron density to.3% of the central electron density. The two argon density profiles that are employed are shown in Panel a) of Fig. 4. As shown in the Panels b) and c) of Fig. 4, the result of the increased argon density is a predicted 1 MW decrease in fusion power and a 1 MW increase in radiated power at time t = 1 sec. In the standard case of.14% of the central electron density, the radiative power losses are found to be approximately 24 MW of bremsstrahlung, 1.5 MW of cyclotron and 5.5 MW of line radiation. Although the increase in argon concentration results in a decrease in fusion power and an increase

4 4 Heating Power (MW) a) Beam Heating of Electrons ICRF Heating of Ions Beam Heating of Ions ICRF Heating of Electrons Fast Ion Thermalization Current (MA) b) Total Current Ohmic Current Bootstrap Current Beam Current ICRF Current Time (seconds) Time (seconds) Current Density (Amps/cm 2 ) c) 41T14 t = 1 s = 5 kev Total Current Density Ohmic Current Density Bootstrap Current Density Beam Current Density ICRF Current Density Current (MA) d) 41T14 t = 1 s = 5 kev Total Current Ohmic Current Bootstrap Current Beam Current ICRF Current ρ (t = 1 s) ρ (t = 1 s) FIG. 1. a) Predicted components of heating and b) predicted components of plasma current as a function of time c) predicted components of current density and d) predicted components of plasma current within a plasma radius as a function of radius at time t = 1 sec in the simulation of the ITER H-mode discharge for pedestal temperature 5. kev. Fusion Density Rate x 1-17 (N/m 3 /s) a) = 5keV ρ (t = 1 s) Fusion Production x 1-2 (N/s) b) = 5 kev ρ (t = 1 s) FIG. 2. (a) Density of fusion neutrons produced per second (b) rate of neutrons produced within a given radius at time t = 1 sec simulated for pedestal temperature 5. kev.

5 5 Electron Density x 1-2 (m -3 ) a) 41T5 41T14 High Density Case Low Density Case Argon Density x 1-17 (m -3 ) a) 41K4 41T14 n Ar =.3% n e n Ar =.14% n e ρ (t = 1 s) ρ (t = 1 s) 1 b) 41T5 41T14 T Ped = 5 kev 5. b) 41K4 41T14 Fusion Power (MW) n e = 1.5 x 1 2 m -3 n e =.91 x 1 2 m -3 Radiated Power (MW) n Ar =.3% n e n Ar =.14% n e Time (seconds) FIG. 3. a) The high electron density (n e = m 3 ) and low electron density (n e = m 3 ) as a function of normalized radius label (ρ) at time t = 1s. b) Fusion power production for the high and low density cases versus time for the pedestal temperatures 5. kev. in radiated power, the increased argon concentration has the beneficial effect of reducing the heat load on the divertor. C. Dependence of Fusion Power Production on Choice of Radio Frequency Heating The sensitivity of the predicted production of fusion power to choice of radio frequency heating is investigated by carrying out three simulations. In each of the simulations the total input heating power is the same 53 MW, and the input neutral beam power is fixed at 33 MW. However, in each of the simulations a different choice is made for the source of the 2 MW of radio frequency power. The choices considered for the radio frequency heating are ion cyclotron heating, electron cyclotron heating, and lower hybrid heating. Results ob- Fusion Power (MW) Time (seconds) c) 41T14 41K4 n Ar =.3% n e n Ar =.14% n e Time (seconds) FIG. 4. a) The argon density as a function of normalized radius ρ for the simulations with a high central argon density (n Ar =.3%n e) and low central argon density (n Ar =.14%n e) at time t = 1s. In these simulations the pedestal temperatures is taken as 5. kev during the H-mode phase; b) Radiated power as a function of time for the two argon density cases consider; and c) Illustrates the dependence of the fusion power produced as function of time in the simulations carried out with the two argon density profiles shown in panel a).

6 6 Fusion Power (MW) T18; 41T12; 41T21 33MW NB + 2MW ICRF 33MW NB + 2MW ECRF 33MW NB + 2 MW LH Time (seconds) T i (kev) a) 45,46,47 = 5keV = 4keV = 3keV ρ (t = 1 s) FIG. 5. Fusion power production as a function of time for different choices of radio frequency heating and the pedestal temperature equal to 5. kev after the L-H transition. The solid line indicates the fusion power obtained in the simulation with ion cyclotron heating, the dashed curve, the fusion power with electron cyclotron heating, and the dotted curve the fusion power obtained in the simulation with lower hybrid heating. T e (kev) b) 45,46,47 = 5keV = 4keV = 3keV tained for the predicted fusion power are relatively insensitive to choice of input radio frequency power. At 1 sec., approximately 5 MW more fusion power is predicted with electron cyclotron heating compared to ion cyclotron heating or lower hybrid heating. This difference is primarily due to the difference in electron and ion heating profiles associated with the electron cyclotron heating compared to the profiles associated with ion cyclotron and lower hybrid heating. The dependence of the fusion power production on the choice of radio frequency heating is illustrated in Fig. 5. D. Dependence of Fusion Power on Pedestal Temperature In order to examine the dependence of fusion power production on the pedestal temperature,, values of 3, 4, or 5 kev are considered for the electron and ion temperatures at the top of the H-mode pedestal. In the simulations, is applied at the radial boundary ρ.97. It has been shown that the suppression of mictroturbulence occurs 32 when the Hahm-Burrel E B flow shear rate 33 is greater than the maximum growth rate of all the drift modes. This result is used to simulate the E B flow shear mechanism in MMM7.1 by using the reduced growth rate, γ E B Hahm Burrel flow shear rate, in the simulation of turbulent transport coefficients. Here, γ is the maximum linear growth rate of the ITG/TEM modes computed in the absence of E B flow shear. In order to study the influence that E B flow shear has on the dependence of fusion power production on Fusion Power (MW) ρ (t = 1 s) 5 c) 45,46,47 = 5 kev = 4 kev = 3 kev Input heating power Time (seconds) FIG. 6. a) Ion temperature profiles and (b) electron temperature profiles and c) fusion power production predicted in simulations of ITER H-mode scenario with E B flow shear rate set equal to zero. In these simulations, the pedestal temperatures are 5. kev (solid line), 4. kev (dashed line), and 3. kev (dot-dashed line).

7 7 pedestal temperature, simulations are first carried out with E B flow shear rate set equal to zero. In these simulations it is found that the fusion power, as might be expected, is much lower than when the E B flow shear rate is used to reduce growth rate in the simulation of the turbulent transport coefficients. The simulations are then repeated with the toroidal rotation frequency ω ϕ computed using the MMM7.1 module and with the E B flow shear rate effect included resulting in a reduced growth rate. It is shown below that when the flow shear rate effect is included in the simulation, there is essentially no dependence of fusion power production on the pedestal hight for the range of pedestal heights considered. In Figs. 6a and 6b, the simulated ion and electron temperature profiles are plotted at t = 1 sec for the three values of the temperature pedestal height (3. kev, 4. kev, and 5. kev) when E B flow shear rate is set equal to zero. The profiles are found to be sensitive to the pedestal height in that a higher pedestal temperature results in a higher central temperature. This indicates tight coupling of core and edge regions of the plasma which can be due to the stiff transport. As a consequence of the higher ion temperature associated with higher pedestal temperature, fusion power production is found to increase with increasing pedestal temperature as shown in Fig. 6c. It can be seen that changes to the edge plasma temperature have a multiplicative effect on the fusion power production. A change in the pedestal temperature from 3 kev to 5 kev results in an increase the fusion power production from 51 MW to 172 MW. The results show that higher pedestal temperature in ITER discharges will be beneficial, particularly due to the low toroidal rotation expected in the ITER discharges. In Fig. 6c, it is found that fusion power production as a function of time is approximately in steady state after t = 28 sec. The fusion power production is determined mainly by the ion temperature and density profiles. Since any temporary increase or decrease in fusion power produces relatively little change in the ion temperature profile, the fusion power production quickly returns to its quasi-steady state value. In fact, once the plasma is heated to the point where it produces a significant amount of fusion self-heating, the fusion power production becomes relatively insensitive to externally applied heating. Hence, stiff transport facilitates fusion ignition and inhibits fusion reaction runaway. The effect of E B flow shear on the dependence of fusion power production on pedestal temperature is illustrated by repeating the simulations with the growth rate reduced by including the E B flow shear rate and with the toroidal rotation frequency, ω ϕ, computed using the MMM7.1 module. The pedestal is again varied in the range 3 to 5 kev. The results of these simulations are shown in Fig.7a-7d where the predicted ion and electron temperatures and the toroidal rotation frequency (ω ϕ ) are plotted as a function of plasma radius and the resulting fusion power is plotted as a function of time. Note that when flow shear effects are included, a core transport barrier, referred to as an Internal Transport Barrier (ITB) is evident in the electron and ion temperature profiles as well as in the toroidal rotation frequency profile. The fusion power production as a function of time is shown in Fig. 7d is found to be approximately 599 MW at t = 1 sec for all three pedestal heights. With an input power of a total of 53 MW, the fusion Q, defined as the ratio of the fusion power divided by the applied heating power, is As expected, the fusion power production obtained when flow shear effects are included, shown in Fig. 7d, is significantly greater than that obtained with the flow shear effect omitted, shown in Fig. 6c. The lack of sensitivity of results to pedestal temperature, indicated in Fig. 7, can be explained as follows: Although one might anticipate, that with a stiff transport model, significant increase in temperature and fusion production with increasing pedestal temperature, this effect is countered by the fact that an increased pedestal temperature results in an increased edge bootstrap current and consequently a decrease in core current when the discharge has the total plasma current that is held fixed. This is shown in Fig. 8a, in which the total plasma current density is plotted as a function of the square root of toroidal flux illustrating the increase in edge current associated with increased edge bootstrap current and the changes in core current. The formation of an ITB in temperature profiles can also be the result of stabilizing effects of low magnetic shear on an anomalous transport. The formation of ITB in temperature profile can also be due to an occurrence of ITB in the toroidal rotation profiles (see e.g. Fig. 7c and Fig. 7d which result in increasing the flow shear and hence reducing the transport and increasing the temperature profiles. The magnetic-q profile shown in Fig. 8b, is found to be the same for all pedestal temperatures considered due to the adjustment of the total current density. In regions where q < 1, the Porcelli model 34 is used to trigger sawtooth crashes and the effect of each sawtooth crash is computed using the KDSAW model 35. Another reason for the insensitivity of fusion power production to pedestal temperature may be due to the over-prediction of the E B flow shear rate resulting from an over-prediction of the toroidal rotation frequency. The predicted toroidal rotation frequency in the plasma center of more than 25 krads/sec (shown in Fig. 7c) might be a over-prediction based on the size of ITER. The evolution of temperature profiles obtained using the MMM7.1 anomalous transport model has been validated using DIII-D, JET and TFTR data 36. However, the prediction of toroidal rotation frequency is not as thoroughly validated as are the temperature predictions. Notice that an internal transport barrier does not occur in the simulated temperature profiles when flow shear effects turned off. Hence, the rotation or the flow shear is more important than the low magnetic shear for the formation of ITB in the temperature profiles.

8 8 T i (kev) a) 41T14 41T17 41T18 = 5keV = 4keV = 3keV T e (kev) b) 41T14 41T17 41T18 T PED = 5 kev T PED = 4 kev T PED = 3 kev ρ (t = 1 s) ρ(t = 1 s) ω φ (krad/s) c) 41T14 41T17 41T18 = 5 kev = 4 kev = 3 kev Fusion Power (MW) d) 41T14, 41T17, 41T18 = 5keV = 4keV = 3keV ρ (t = 1 s) Time (seconds) FIG. 7. a) Ion temperature profiles and b) electron temperature profiles c) toroidal rotation frequency and d) fusion power production predicted in simulations of ITER H-mode scenario with E B flow shear rate included. In these simulations, the pedestal temperatures are 5. kev (solid line), 4. kev (dashed line), and 3. kev (dot-dashed line). E. Sensitivity of Fusion Power on E B Flow Shear Rate Simulations in which the pedestal temperature was varied were carried out without and with the flow shear effect included. In the simulations with the E B flow shear effect included, there is the possibility that there is an over-prediction of the reduction in growth rate resulting in an over-prediction of plasma confinement and, consequently, an over-prediction of fusion power production. In order to examine the sensitivity regarding the possible uncertainty in the computation of the flow shear rate, simulations are carried out with the coefficient α multiplying the E B flow shear rate. Thus, growth rate associated with the turbulent transport is γ αe B in the simulations presented below. In Fig. 9a, the toroidal rotation frequency, ω ϕ, which contributes to E B flow shear turbulence stabilization, is plotted as function of radius at time t = 1 sec for values of flow shear coefficient α equal to.25,.5,.75 and 1.. The toroidal rotation frequency and toroidal momentum transport are evolved using Weiland component in MMM7.1 anomalous transport module. The toroidal momentum transport is found to be larger at the center of plasma and smaller in the edge. These simulations are carried our for the high density plasma considered in subsection A above, that is for a plasma with a central density n e = m 3 The poloidal rotation frequency, which also contributes to flow shear is calculated using NCLASS module. The flow shear coefficient with α =. corresponds to the case with E B flow shear stabilization is turned off and α = 1. yields the flow shear coefficient computed using the MMM7.1 transport module. Based on rotation measurements in DIII-D experiment, the toroidal frequency is set equal to 3 krad/s at ρ =.8, and the simulations describe the evolution in

9 9 Total Current Density (Amps/cm 2 ) a) = 5 kev = 4 kev = 3 kev 41T14 41T17 41T ρ (t = 1 s) q b) 41T14 41T17 41T18 = 5 kev = 4 kev = 3 kev ρ (t = 1 s) FIG. 8. a) Total plasma current density and b) magnetic-q profiles for ITER H-mode scenario with the pedestal temperatures 5. kev (solid line), 4. kev (dashed line), and 3. kev (dot-dashed line) are plotted as a function of radius. the region ρ = to ρ =.8. In the region ρ =.8 to ρ = 1. TSC data is used. In contrast to above simulations where PEDESTAL module is used, in these simulations the temperature pedestal height in the TSC data is set equal to 5. kev. Note that, as shown in Fig. 9b, the plasma current density tends toward zero at ρ = 1.. The simulated ion and electron temperature profiles at time t = 1 sec are shown for the different flow shear coefficients in Figs. 9c and 9d. The formation of internal transport barriers (ITBs) are found for larger flow shear coefficients (α =.75 and α = 1.) due to the larger toroidal rotation frequencies for these values of α as seen in Fig. 9a. The location of the ITBs are in the radial regions where the gradients of the toroidal rotation frequency are steep. This indicates that turbulent transport is significantly reduced in those regions of the plasma where flow shear is sufficiently strong. Local regions of strong flow shear are associated with the formation of transport barriers. The formation of the ITBs in the electron temperature profiles are less pronounced than the ITBs in the ion temperature profiles. This is a consequence of the fact that, in the simulations, there is no E B flow shear suppression of the ETG modes due to the short wavelength nature of the ETG modes. Since the ETG modes are unaffected by E B flow shear suppression, the electron temperatures in the core is found to be lower than the ion temperatures. ITBs are not found in ion or in the electron temperature profiles for the case with E B flow shear turned off (α =.), Figs. 6a and 6b. Similarly ITBs are not found for the case with flow shear coefficient set equal to one-quarter or one-half (α =.25 and α =.5). This indicates that the formation of ITB in ITER discharges might be an issue for discharges with low E B flow shear. The predicted fusion power is shown as a function of time in Fig. 9e for the values of α considered. In these simulations of ITER H-mode discharges, the fusion power production is found to be 3 MW for α =.25, 378 MW for α =.5, 663 MW for α =.75 and 848 MW for α = 1. (similar to the result presented in Fig. 3b. Predicted fusion power ranges from 3 MW with no flow shear stabilization to 85 MW with flow shear coefficient equal to 1. (MMM7.1-predicted rotation). These results indicate the importance of flow shear for ITER successfully obtaining the goal of fusion Q = 1. IV. SUMMARY The ITER H-mode DT time-dependent integrated predictive whole device simulations are carried out using the PTRANSP code with boundary conditions obtained from the TSC code. Feedback loops are used in the TSC code to control the plasma boundary position and shape while constraints are used for the maximum allowed coil currents. The prescribed-boundary version of the TEQ module is used to compute the self-consistent evolution of the equilibrium. Auxiliary heating sources are computed using the NTCC NUBEAM module for neutral beam injection, the TORIC full wave module for ICRH, the TORAY module for electron cyclotron, the LSC 1- D Fokker Planck module for lower hybrid, and PREACT for nuclear heating. Atomic physics cross sections for ionization, recombination, and impurity radiation are computed using ADAS module. Thermal and toroidal angular momentum anomalous transport is computed using the Multi-Mode MMM7.1 anomalous transport model. The NCLASS module is used to compute neoclassical ion thermal transport as well as neoclassical resistivity and bootstrap current. The evolution of the current density and magnetic q profiles are computed by advancing a magnetic diffusion equation. The L- to H-mode threshold

10 1 Rotation Frequency, ω φ (krad/s) a) T3,T37,T32,T26 α = 1. α =.75 α =.5 α = ρ (t = 1s) Total Current Density (Amps/cm 2 ) b) T3,T37,T32,T26 α = 1. α =.75 α =.5 α = ρ(t= 1 s) 5 4 c) T3,T37,T32,T26 α = 1. α =.75 α =.5 α = d) T3,T37,T32,T26 α = 1. α =.75 α =.5 α =.25 T i (kev) 3 2 T e (kev) ρ(t = 1 s) ρ(t = 1 s) 1 e) T3,T37,T32,T26 Fusion Power (MW) α = 1. α =.75 α =.5 α = ρ (t = 1 s) FIG. 9. a) The toroidal rotation frequency profile b) current density profile c) ion temperature profiles (d) electron temperature profile and e) fusion power production in which different flow shear coefficient (α =1.,.75,.5,.25) were set at ρ =.8. These ITER H-mode simulations are carried out using the pedestal temperatures 5. kev.

11 11 heating power is computed using the PEDESTAL model and an automated transition from L- to H mode is triggered when the total power exceeds the empirically determined power threshold. The pedestal height is varied about the value computed using the EPED1 code. Simulations have been carried out to investigate the dependence and sensitivity of fusion power production in ITER H-mode discharges on electron density, argon impurity concentration, choice of radio frequency heating, pedestal temperature and degree of plasma rotation. The fusion power is found to increase with an increase in the electron density. A decrease in fusion power and an increase in radiated power occurs if the central argon impurity density is increased from.14% of the central electron density to.3% of the central electron density. The increased in argon density results in a predicted 1 MW decrease in fusion power and a 1 MW increase in radiated power at time t = 1 sec. In the study of dependence of fusion power production on choice of radio frequency heating, approximately 5 MW more fusion power is predicted with electron cyclotron heating compared to ion cyclotron heating or lower hybrid heating. The fusion power production is found to be sensitive to the height of the pedestal temperature in the absence of E B flow shear reduction of the turbulence growth rate, but fusion power production is found to be insensitive to the height of the pedestal in the presence of E B flow shear rate reduction is included. The insensitivity of fusion power production when the E B flow shear stabilization effect is included may be a consequence of over-prediction of E B flow shear. The degree of plasma rotation is studied by varying the E B flow shear coefficient. It is found that a large values of flow shear is necessary for the formation of ITB and for achieving a fusion Q equal to 1. In the absence of flow shear the maximum fusion Q attained is equal to 5.7 in the simulations carried out in this study. V. ACKNOWLEDGEMENTS The authors would like to thank Philip Snyder for providing the EPED1 prediction of ITER H-mode pedestal pressure. The research carried out, yielding the results presented in this paper, is supported by the U.S. Department of Energy, Office of Science, under Award Number DE-FG2-92-ER C. Kessel, G. Giruzzi, A. Sips, R. Budny, J. Artaud, V. Basiuk, F. Imbeaux, E. Joffrin, M. Schneider, M. Murakami, T. Luce, H. S. John, T. Oikawa, N. Hayashi, T. Takizuka, T. Ozeki, Y.-S. Na, J. Park, J. Garcia, and A. Tucillo, Nuclear Fusion 47, 1274 (27). 2 T. Rafiq, A. H. Kritz, G. Bateman, C. Kessel, D. C. McCune, and R. V. Budny, Physics of Plasmas 18, (211). 3 A. Kritz, T. Rafiq, C. Kessel, G. Bateman, D. McCune, R. Budny, and A. Pankin, Nuclear Fusion 51, 1239 (211). 4 A. C. C. Sips, G. Giruzzi, S. Ide, C. Kessel, T. C. Luce, J. A. Snipes, J. K. 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13 Time (seconds) Heating Power (MW) a) Beam Heating of Electrons ICRF Heating of Ions Beam Heating of Ions ICRF Heating of Electrons Fast Ion Thermalization

14 Time (seconds) Current (MA) b) Total Current Ohmic Current Bootstrap Current Beam Current ICRF Current

15 ρ (t = 1 s) Current Density (Amps/cm 2 ) c) 41T14 t = 1 s = 5 kev Total Current Density Ohmic Current Density Bootstrap Current Density Beam Current Density ICRF Current Density

16 ρ (t = 1 s) Current (MA) d) 41T14 t = 1 s Total Current Ohmic Current Bootstrap Current Beam Current ICRF Current = 5 kev

17 Fusion Density Rate x 1-17 (N/m 3 /s) a) = 5keV ρ (t = 1 s)

18 Fusion Production x 1-2 (N/s) b) = 5 kev ρ (t = 1 s)

19 ρ (t = 1 s) Electron Density x 1-2 (m -3 ) a) 41T5 41T14 High Density Case Low Density Case

20 Time (seconds) 1 b) 41T5 41T14 T Ped = 5 kev Fusion Power (MW) n e = 1.5 x 1 2 m -3 n e =.91 x 1 2 m -3

21 3. a) 41K4 41T14 Argon Density x 1-17 (m -3 ) n Ar =.3% n e n Ar =.14% n e ρ (t = 1 s)

22 Time (seconds) 5. b) 41K4 41T14 Radiated Power (MW) n Ar =.3% n e n Ar =.14% n e

23 Time (seconds) 7 6 c) 41T14 41K4 Fusion Power (MW) n Ar =.3% n e n Ar =.14% n e

24 7 41T18; 41T12; 41T21 6 Fusion Power (MW) MW NB + 2MW ICRF 33MW NB + 2MW ECRF 33MW NB + 2 MW LH Time (seconds)

25 ρ (t = 1 s) T i (kev) a) 45,46,47 = 5keV = 4keV = 3keV 5

26 ρ (t = 1 s) T e (kev) b) 45,46,47 = 5keV = 4keV = 3keV 5

27 Time (seconds) Fusion Power (MW) c) 45,46,47 = 5 kev = 4 kev = 3 kev Input heating power

28 ρ (t = 1 s) T i (kev) a) 41T14 41T17 41T18 = 5keV = 4keV = 3keV 1

29 ρ(t = 1 s) T e (kev) b) 41T14 41T17 41T18 T PED = 5 kev T PED = 4 kev T PED = 3 kev 1

30 ρ (t = 1 s) ω φ (krad/s) c) 41T14 41T17 41T18 = 5 kev = 4 kev = 3 kev 5

31 Time (seconds) Fusion Power (MW) 7 d) T14, 41T17, 41T18 = 5keV = 4keV = 3keV

32 Total Current Density (Amps/cm 2 ) a) = 5 kev = 4 kev = 3 kev 41T14 41T17 41T ρ (t = 1 s)

33 ρ (t = 1 s) q b) 41T14 41T17 41T18 = 5 kev = 4 kev = 3 kev 1

34 Rotation Frequency, ω φ (krad/s) a) T3,T37,T32,T26 α = 1. α =.75 α =.5 α = ρ (t = 1s)

35 Total Current Density (Amps/cm 2 ) b) T3,T37,T32,T26 α = 1. α =.75 α =.5 α = ρ(t= 1 s)

36 ρ(t = 1 s) 5 4 c) T3,T37,T32,T26 α = 1. α =.75 α =.5 α =.25 T i (kev) 3 2 1

37 ρ(t = 1 s) 5 4 d) T3,T37,T32,T26 α = 1. α =.75 α =.5 α =.25 T e (kev) 3 2 1

38 1 e) T3,T37,T32,T26 Fusion Power (MW) α = 1. α =.75 α =.5 α = ρ (t = 1 s)