New short XGC-0 simulations are submitted on FRANKLIN in the debug mode. The case XGC-210 is based on the case XGC-209. The case XGC-211 uses modified source code where smoothing for the radial electric field is done for three neighboring grid points instead of one (as in the case XGC-210).
IF ( fm_nsmooth_er > 0 ) THEN
DO i=1, fm_nsmooth_er
CALL smoothb0( z_e_radial, diag_flow_npsi, 3 )
ENDDO
ENDIF
The radial electric field profiles as well as flow shear rates are significantly smoother comparing to the case where is smoothing is done over one neighboring grid point.
Results that use the same smoothing in the plasma core, but use averaging over one neighboring points are given below for comparison.
Significant particle losses noted in the last two posts are studied by analyzing the diffusivity profiles.
The particle diffusivity remains too high after 13999 time steps, which correspond to approximately 28 toroidal ion transit times (13999×0.002). Thermal diffusivity remains very high as well. However, the ion and electron temperatures continue to rise with very high auxiliary heating power.
Smoothing of thermal diffusivity profiles (fm_nsmooth_chi=2) improves numerical stability.
The flow shear factor is zero in the plasma core. Also, the flow shear factor remains relatively noisy.
Two new cases are submitted on FRANKLIN in order to investigate different settings for smoothing.
Case XGC-208 is based on the case XGC-206, except of fm_nsmooth_chi that is increased from 1 to 2.
Case XGC-209 is submitted to test new procedure to smooth the radial electric field profiles. In addition to the parameter fm_nsmooth that is kept 1 (as in the previous cases), the following settings are used:
fm_nsmooth_er = 4 ! number of smoothing for radial electric field in the core refion
fm_smooth_er_rhob = 0.95 ! rho where transition between different level of smoothing is applied
fm_smooth_er_coef = 75. ! coefficient that controls sharpness of transition between different level of smoothness for Er
fm_nsmooth_chi = 2 ! number of applications of diffusivity smoothing in fmcfm_call
Set of simulations where particle bounce on the inner boundary was disabled is complete. The results indicate reduction of particle near the magnetic axis. The radial electric field has significant oscillations near the magnetic axis.
New procedure for smoothing of radial electric field profile is implemented in the fmcfm_call routine. Different levels of smoothing is applied in the plasma core and in the plasma edge. The radial electric field profile in the plasma edge is smoothed fm_nsmooth times together other plasma profiles such as electron and ion temperatures and plasma density profiles. The radial electric field in the plasma core is smoothed fm_nsmooth_er times. The new smoothed profiles are merge together using the following formula:
and used in the computation of the flow shear. Here, is the coefficient that describes sharpness of the transition between two smoothed profiles The fm_smooth_er_coef is used to set this coefficient in the XGC-0 code through the namelist. The parameter controls the location of the transition. The fm_smooth_er_rhob variable is used to set this parameter in the code. The default values for these parameters are: and .
Case XGC-204 crashed after 65000 time steps. It is possible that time limit for this simulation has been set incorrectly.
Case XGC-205 crashed after 50000 time steps. Same reason (?)
Profiles for plasma density, temperatures and electric field are given below.
Radial electric field remains very noisy in the plasma core. Both the radial electric field and plasma density profiles are found to be very different comparing to the case when electron dynamics has been diabled (case XGC-203).
Previous XGC-0 results with with electron dynamics disabled show significant difference in radial electric field profiles. Simulations with electron disabled has larger values for radial electric field in the plasma core. It looks that there is a charge separation in the plasma core (see Fig 1).
Fig. 1. Case XGC-203: DIII-D discharge 136674.01405; no electrons; 80 radial zones
Two new simulations are submitted on Franklin:
XGC-204 for the DIII-D discharge 096333.0333, and
XGC-205 for the DIII-D discharge 136674.01405.
Another problem that needs to be address is particle losses (see Fig. 2).
Some changes to the code includes increased number of radial zones for radial electric field:
efld_npsi is increased from 35 to 70 in modules.F90
Gunyoung suggested to disable the bounce operation from
the simulation inner boundary in the simulations that include magnetic axis. Cases XGC-200 — XGC-205 don’t include the magnetic axis and start at sml_inpsi equal to 0.01.
Fig. 2. Case XGC-203: DIII-D geometry g136674.01405; 80 radial zones; no electrons.
![{Huge E_r} = displaystylefrac{1}{2} left[ E_r^{rm core} left( 1 - tanh(C_{er} (rho-rho_b)) ) + E_r^{rm edge} ( 1 + tanh(C_{er} (rho-rho_b)) right) right]](http://s0.wp.com/latex.php?latex=%7BHuge+E_r%7D+%3D+displaystylefrac%7B1%7D%7B2%7D+left%5B+E_r%5E%7Brm+core%7D+left%28+1+-++tanh%28C_%7Ber%7D+%28rho-rho_b%29%29+%29++%2B+E_r%5E%7Brm+edge%7D+%28+1+%2B+tanh%28C_%7Ber%7D+%28rho-rho_b%29%29+right%29+right%5D&bg=ffffff&fg=000000&s=0 "{Huge E_r} = displaystylefrac{1}{2} left[ E_r^{rm core} left( 1 - tanh(C_{er} (rho-rho_b)) ) + E_r^{rm edge} ( 1 + tanh(C_{er} (rho-rho_b)) right) right]")
flow shear. Here, 
is the coefficient that describes sharpness of the transition between two smoothed profiles The fm_smooth_er_coef is used to set this coefficient in the XGC-0 code through the namelist. The 
parameter controls the location of the transition. The fm_smooth_er_rhob variable is used to set this parameter in the code. The default values for these parameters are: 
and 
.
