Integrated Modeling of Tokamak Plasmas

DIII-D 132014

&tbl_param             ! (anomalous) turbulence diffusion
tbl_diffusion_on=1     ! 0: no turbulence diffusion, 1: simple turbulence diffusion
tbl_diffusion_mode=3   ! 1 = random walk model, 2 = advection-diffusion model
! mode=2 enables separate control of particle and heat diffusion
tbl_stop_time=500000   ! Stop the turbulence diffusion
tbl_period = 1       ! frequency of calling turbulence diffusion and 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=0.93D0  ! D_turb profile center
tbl_d_profile_psiwid=0.02D0  ! D_turb profile full width
tbl_d_profile_psicen2=0.999D0  ! 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=0.03D0      ! m^2/sec, outside (pedestal bottom) value of D_turb
tbl_D_coeff2=0.6D0     ! 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=0.9D0    ! m^2/sec, thermal D_turb for outside of separatrix (SOL+private flux region) for ions

! electron thermal diffusivities
tbl_therDe_coeff_in=0.8D0    ! m^2/sec, inside (pedestal top) value of thermal D_turb for electrons
tbl_therDe_coeff=-0.1D0    ! 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

DIII-D 132016

&tbl_param             ! (anomalous) turbulence diffusion
tbl_diffusion_on=1     ! 0: no turbulence diffusion, 1: simple turbulence diffusion
tbl_diffusion_mode=3   ! 1 = random walk model, 2 = advection-diffusion model
! mode=2 enables separate control of particle and heat diffusion
tbl_stop_time=500000   ! Stop the turbulence diffusion
tbl_period = 1       ! frequency of calling turbulence diffusion and 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=0.999D0  ! 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=-0.05D0    ! 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
/

DIII-D 132017

&tbl_param             ! (anomalous) turbulence diffusion
tbl_diffusion_on=1     ! 0: no turbulence diffusion, 1: simple turbulence diffusion
tbl_diffusion_mode=3   ! 1 = random walk model, 2 = advection-diffusion model
! mode=2 enables separate control of particle and heat diffusion
tbl_stop_time=500000   ! Stop the turbulence diffusion
tbl_period = 1       ! frequency of calling turbulence diffusion and 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=0.91D0  ! 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=0.3D0     ! 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=0.001D0    ! m^2/sec, outside (pedestal bottom) value of thermal D_turb for ions
tbl_therDi_coeff2=0.5D0    ! 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=-0.1D0    ! 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
/

DIII-D 132018

&tbl_param             ! (anomalous) turbulence diffusion
tbl_diffusion_on=1     ! 0: no turbulence diffusion, 1: simple turbulence diffusion

tbl_diffusion_mode=3   ! 1 = random walk model, 2 = advection-diffusion model
! mode=2 enables separate control of particle and heat diffusion
tbl_stop_time=500000   ! Stop the turbulence diffusion
tbl_period = 1       ! frequency of calling turbulence diffusion and 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=0.89D0  ! 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=1D0     ! m^2/sec, D_turb for outside of separatrix (SOL+private flux region)

! ion thermal diffusivities
tbl_therDi_coeff_in=0.5D0    ! m^2/sec, inside (pedestal top) value of thermal D_turb for ions
tbl_therDi_coeff=0.001D0    ! m^2/sec, outside (pedestal bottom) value of thermal D_turb for ions
tbl_therDi_coeff2=2.0D0    ! m^2/sec, thermal D_turb for outside of separatrix (SOL+private flux region) for ions

! electron thermal diffusivities
tbl_therDe_coeff_in=.8D0    ! 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=0.2D0    ! m^2/sec, thermal D_turb for outside of separatrix (SOL+private flux region) for electrons
/

The effect of neutrals is studied for the discharge DIII-D 132016. The heat load width is relatively weekly affected by the neutral collisions.

Summary, the effect of neutrals are rather small comparing to the anomalous effects.

These summary plots DIII-D and Alcator C-Mod discharges are based on Julian and my simulations. NSTX discharges are simulated by Gunyoung. I have to redo all simulations for the DIII-D discharge 132018 due to insufficient resolution in lim_store_mz_in/out (the resulution has increased to 500/1500. It looks like that lambda_div is consistently decreasing with the plasma current.

The DIII-D plot has been updated on August 27. Parameters associated with the electron dynamics modeling has been corrected.

has been scaled with the factor that was varied from 0.3 to 1.5. The neutral collisions, anomalous diffusion, heating, and radiation losses have been disable for this scan. Also, the electron background profile has been fixed in these simulations (col_varying_bg_elec=0). The divertor heat flux width, , is shown as a function of the multiplier, on the figure below.

The radial electric field profiles for three different values of C_bp are shown below:

C_bp=0.75

C_bp=1.00

C_bp=1.50

I reran Alexei’s case number XGC-B35 on jaguar at NCCS, essentially unchanged from how he ran it on hopper at NERSC previously except for using a different number of processes.  The results are fairly similar at my final run time of 80 ion transit times (see plots).  We should probably turn on NBI heating for the ions to maintain the proper ion temperature near psi_min.  This run had a neutrals birth temperature of 10 eV.  It is not clear how to further improve the profile behavior near the separatrix.

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: