Smoothing algorithm is modified

Smoothing procedure adopted from the ASTRA code on Friday (see previous post) is tested for set of 200 random numbers. The plots are generated for the smoothness parameter alpha=0.001 (left figure), alpha=0.001 (center figure), and alpha=0.001 (left figure):

In order to introduce more smoothing in the plasma core which is needed to compensate additional numerical noise in the core introduced by volume effect, alpha dependence on rho is introduced:

alpha(rho) = alpha_0 (1-rho/rho_{edge})^beta

where beta is the coefficient that controls region where smoothing is applied. The following function is selected for the next test:

f(rho)=displaystyle{3-2rho^3-50exp^{-displaystylefrac{(rho-rho_b)^2}{Delta}} + 40 frac{R}{1+9rho^2}}

where R is a random number in the range from 0 to 1, rho_0 and Delta are the coefficient that are set to 0.95 and 0.001 correspondingly. This function reproduce XGC-0 results for the radial electric field with more noise in the plasma core and large potential well in the plasma edge. The goal of smoothing is to remove noise in the plasma core and to preserve the details of potential well in the plasma edge. The results on the figure below are obtained for smoothness parameters alpha_0=0.01 and beta=4.

The level of smoothness in the plasma core is controlled by alpha_0 and the region where soothing is applied is controlled by the coefficient beta. Smaller values of beta should result in more extended region where the smoothing is applied. Test below show results for the same alpha_0, but beta set to 2.

3 – 2 rho^3