Integrated Modeling of Tokamak Plasmas

These simulations continue our efforts to understand the neoclassical prediction of the heat load on the divertor plates for the DIII-D and Alcator C-Mod discharges. In our previous studies with the anomalous transport included, we have found that the temperature of neutrals change the rate of the pedestal build up. However, the final pedestal profiles that were limited by the ideal stability conditions that were analyzed with the ELITE code are found independent of the neutral temperature. It turns out that the neoclassical case is different. Without additional dissipation from the anomalous transport, the plasma density profiles become too sharp just before the separatrix. After discussing this problem with Gunyoung, the initial temperature of neutrals have been reduced from 50 eV to 3 eV (Compton temperature). The plasma profiles looks more reasonable. However, there is still spiky in the ion temperature profile just after the seperatrix and there is a deep in the plasma
density profile in the separatrix region. The heat load profiles looks more realistic as well (except of the electron particle flux for the inner divertor plate). The results below are given for the DIII-D discharge 132016.03023 (case XGC-B35).

There are a problem with reproducing ion temperature profiles. For example, the ion thermal diffusivity is set to zero in our simulation for the DIII-D discharge 132018.01948. The ion temperature significantly drops after 10 ion transit times:

The comparison with experimental profiles has been improved through using eq_nmass1=2  option. Also, the simulations have been run for longer times (20 ion transit times vs 14 ion transit times as before). Some diffusivities differ significantly from the prevous scan

132016.03023

&tbl_param             ! (anomalous) turbulence diffusion

tbl_diffusion_on=1     ! 0: no turbulence diffusion, 1: simple turbulence diffusion
tbl_diffusion_mode=3   ! 1 = random walk, 2 = random walk + anomalous convective velocity
tbl_stop_time=500000   ! Stop the turbulence diffusion
tbl_period = 1       ! frequency of calling fmcfm_call
tbl_d_profile_on=-1     ! 1: spatially varying D_turb profile (tanh), 0: spatially constant profile in pedestal region
tbl_slope_on=0         ! D_turb turned on only within finite poloidal angles (+45 deg) around outside midplane
tbl_d_profile_psicen=0.94D0  ! D_turb profile center
tbl_d_profile_psiwid=0.02D0  ! D_turb profile full width

tbl_d_profile_psicen2=0.995D0  ! D_turb profile center
tbl_d_profile_psiwid2=-0.01D0  ! D_turb profile full width

! particle diffusivities (random walk diffusion coefficients)

tbl_D_coeff_in=0.3D0     ! m^2/sec, inside (pedestal top) value of D_turb
tbl_D_coeff=0.15D0      ! m^2/sec, outside (pedestal bottom) value of D_turb
tbl_D_coeff2=0.5D0     ! m^2/sec, D_turb for outside of separatrix (SOL+private flux region)

! ion thermal diffusivities

tbl_therDi_coeff_in=0.1D0    ! m^2/sec, inside (pedestal top) value of thermal D_turb for ions
tbl_therDi_coeff=0.1D0    ! m^2/sec, outside (pedestal bottom) value of thermal D_turb for ions
tbl_therDi_coeff2=0.9D0    ! m^2/sec, thermal D_turb for outside of separatrix (SOL+private flux region) for ions

! electron thermal diffusivities

tbl_therDe_coeff_in=0.6D0    ! m^2/sec, inside (pedestal top) value of thermal D_turb for electrons
tbl_therDe_coeff=-0.05D0    ! m^2/sec, outside (pedestal bottom) value of thermal D_turb for electrons
tbl_therDe_coeff2=0.9D0    ! m^2/sec, thermal D_turb for outside of separatrix (SOL+private flux region) for electrons

/

Four simulations without anomalous diffusion (tbl_diffusion_on=0) have been submitted on Hopper at NERSC. One simulation crashed after 12750 in the interpolation routines:

istep:        12750

 ?herm2ev:  xget=        NaN out of range  4.4710E-01 to  1.3519E+00
 ?herm2ev:  yget=        NaN out of range -8.5161E-01 to  8.5161E-01
 **EZspline** ERROR/WARNING #           96  occurred
 **EZspline** some error occurred in EZspline_derivative

This problem is still to be sorted out. Other simulations are completed. However, temperature and density profiles looks odd. In particular, there is a bump in the ion temperature profiles just after the separatrix

Results for this higher total plasma current case are given below:

Heat loads in the inner and outer plate regions are computed with XGC0. The results for the inner plates are shown below:

The results for the outer plate are stored incorrectly. This problem with the code needs to be investigated. Also, the ion thermal flux is too noisy despite that more than 3,000,000 particles have been used in this simulation. The heat fluxes are also found to be unexpectingly low.

A set of XGC0 simulations has been run to determine the anomalous transport coefficients that can be used together with the neoclassical transport, which self-consistently computed with XGC0, to reproduce the experimental profiles for four DIII-D current scan discharges. Below the final diffusivity parameters, initial and final profiles are given.

132014.03000

tbl_d_profile_on=-1     ! 1: spatially varying D_turb profile (tanh), 0: spatially constant profile in pedestal region
tbl_slope_on=0         ! D_turb turned on only within finite poloidal angles (+45 deg) around outside midplane
tbl_d_profile_psicen=0.93D0  ! D_turb profile center
tbl_d_profile_psiwid=0.02D0  ! D_turb profile full width
tbl_d_profile_psicen2=0.995D0  ! D_turb profile center
tbl_d_profile_psiwid2=-0.01D0  ! D_turb profile full width


! particle diffusivities (random walk diffusion coefficients)
tbl_D_coeff_in=0.2D0     ! m^2/sec, inside (pedestal top) value of D_turb
tbl_D_coeff=0.01D0      ! m^2/sec, outside (pedestal bottom) value of D_turb
tbl_D_coeff2=0.1D0     ! m^2/sec, D_turb for outside of separatrix (SOL+private flux region)

! ion thermal diffusivities
tbl_therDi_coeff_in=.070D0    ! m^2/sec, inside (pedestal top) value of thermal D_turb for ions
tbl_therDi_coeff=-0.050D0    ! m^2/sec, outside (pedestal bottom) value of thermal D_turb for ions
tbl_therDi_coeff2=0.6D0    ! m^2/sec, thermal D_turb for outside of separatrix (SOL+private flux region) for ions

! electron thermal diffusivities
tbl_therDe_coeff_in=0.8D0    ! m^2/sec, inside (pedestal top) value of thermal D_turb for electrons
tbl_therDe_coeff=0.03D0    ! m^2/sec, outside (pedestal bottom) value of thermal D_turb for electrons
tbl_therDe_coeff2=0.6D0    ! m^2/sec, thermal D_turb for outside of separatrix (SOL+private flux region) for electrons

132016.03023

tbl_d_profile_on=-1     ! 1: spatially varying D_turb profile (tanh), 0: spatially constant profile in pedestal region
tbl_slope_on=0         ! D_turb turned on only within finite poloidal angles (+45 deg) around outside midplane
tbl_d_profile_psicen=0.94D0  ! D_turb profile center
tbl_d_profile_psiwid=0.02D0  ! D_turb profile full width
tbl_d_profile_psicen2=0.995D0  ! D_turb profile center
tbl_d_profile_psiwid2=-0.01D0  ! D_turb profile full width


! particle diffusivities (random walk diffusion coefficients)
tbl_D_coeff_in=0.13D0     ! m^2/sec, inside (pedestal top) value of D_turb
tbl_D_coeff=0.04D0      ! m^2/sec, outside (pedestal bottom) value of D_turb
tbl_D_coeff2=0.3D0     ! m^2/sec, D_turb for outside of separatrix (SOL+private flux region)

! ion thermal diffusivities
tbl_therDi_coeff_in=0.1D0    ! m^2/sec, inside (pedestal top) value of thermal D_turb for ions
tbl_therDi_coeff=-0.05D0    ! m^2/sec, outside (pedestal bottom) value of thermal D_turb for ions
tbl_therDi_coeff2=0.7D0    ! m^2/sec, thermal D_turb for outside of separatrix (SOL+private flux region) for ions

! electron thermal diffusivities
tbl_therDe_coeff_in=0.25D0    ! m^2/sec, inside (pedestal top) value of thermal D_turb for electrons
tbl_therDe_coeff=0.02D0    ! m^2/sec, outside (pedestal bottom) value of thermal D_turb for electrons
tbl_therDe_coeff2=0.7D0    ! m^2/sec, thermal D_turb for outside of separatrix (SOL+private flux region) for electrons

132017.02998

tbl_d_profile_on=-1     ! 1: spatially varying D_turb profile (tanh), 0: spatially constant profile in pedestal region
tbl_slope_on=0         ! D_turb turned on only within finite poloidal angles (+45 deg) around outside midplane
tbl_d_profile_psicen=0.91D0  ! D_turb profile center
tbl_d_profile_psiwid=0.02D0  ! D_turb profile full width
tbl_d_profile_psicen2=0.995D0  ! D_turb profile center
tbl_d_profile_psiwid2=-0.01D0  ! D_turb profile full width


! particle diffusivities (random walk diffusion coefficients)
tbl_D_coeff_in=0.13D0     ! m^2/sec, inside (pedestal top) value of D_turb
tbl_D_coeff=0.015D0      ! m^2/sec, outside (pedestal bottom) value of D_turb
tbl_D_coeff2=0.2D0     ! m^2/sec, D_turb for outside of separatrix (SOL+private flux region)

! ion thermal diffusivities
tbl_therDi_coeff_in=.1D0    ! m^2/sec, inside (pedestal top) value of thermal D_turb for ions
tbl_therDi_coeff=-0.20D0    ! m^2/sec, outside (pedestal bottom) value of thermal D_turb for ions
tbl_therDi_coeff2=0.9D0    ! m^2/sec, thermal D_turb for outside of separatrix (SOL+private flux region) for ions

! electron thermal diffusivities
tbl_therDe_coeff_in=0.35D0    ! m^2/sec, inside (pedestal top) value of thermal D_turb for electrons
tbl_therDe_coeff=-0.01D0    ! m^2/sec, outside (pedestal bottom) value of thermal D_turb for electrons
tbl_therDe_coeff2=1.5D0    ! m^2/sec, thermal D_turb for outside of separatrix (SOL+private flux region) for electrons

132018.01948

tbl_d_profile_on=-1     ! 1: spatially varying D_turb profile (tanh), 0: spatially constant profile in pedestal region
tbl_slope_on=0         ! D_turb turned on only within finite poloidal angles (+45 deg) around outside midplane
tbl_d_profile_psicen=0.89D0  ! D_turb profile center
tbl_d_profile_psiwid=0.02D0  ! D_turb profile full width
tbl_d_profile_psicen2=0.995D0  ! D_turb profile center
tbl_d_profile_psiwid2=-0.01D0  ! D_turb profile full width


! particle diffusivities (random walk diffusion coefficients)
tbl_D_coeff_in=0.05D0     ! m^2/sec, inside (pedestal top) value of D_turb
tbl_D_coeff=0.002D0      ! m^2/sec, outside (pedestal bottom) value of D_turb
tbl_D_coeff2=0.2D0     ! m^2/sec, D_turb for outside of separatrix (SOL+private flux region)

! ion thermal diffusivities
tbl_therDi_coeff_in=0.3D0    ! m^2/sec, inside (pedestal top) value of thermal D_turb for ions
tbl_therDi_coeff=-0.1D0    ! m^2/sec, outside (pedestal bottom) value of thermal D_turb for ions
tbl_therDi_coeff2=0.7D0    ! m^2/sec, thermal D_turb for outside of separatrix (SOL+private flux region) for ions

! electron thermal diffusivities
tbl_therDe_coeff_in=.2D0    ! m^2/sec, inside (pedestal top) value of thermal D_turb for electrons
tbl_therDe_coeff=0.07D0    ! m^2/sec, outside (pedestal bottom) value of thermal D_turb for electrons
tbl_therDe_coeff2=0.7D0    ! m^2/sec, thermal D_turb for outside of separatrix (SOL+private flux region) for electrons

Preliminary results for the particle and heat fluxes in the divertor area for a sequence of times (t=60, 65, 70,75, and 79 ion transit times) are shown below. These results are obtained in relatively long simulation XGC-O15 with increased number of particles.

The anomalous diffusivity profiles that can be used in XGC-0 in order to reproduce the experimental profiles in the Alcator C-Mod discharge 1100212024 are finally found. The particle and thermal diffusivity profiles are shown below. Also, the radial electric field, plasma density and total ion temperature are shown as well. It has been found that the ion temperature profile can be reproduced only if the thermal and particle pinches in the pedestal area is introduced. The results are still to be analyzed. There is a small hump in the density profile that is associated with gradient change in the diffusivity profile at around tbl_d_profile_psicen2.