Double transport barriers pressure profile

An analytic expression for the pressure profile of double (inner and external) transport barriers is given by

$$P (\psi) = a_i \left( 1 + \tanh \left( \frac{- (\psi - \psi_i)}{w... ...+ a_e \left( 1 + \tanh \left( \frac{- (\psi - \psi_e)}{w_e} \right) \right) - c$$ (523)

where $\psi$ is the normalized poloidal flux, $w_i$ and $w_e$ are the width of the inner and external barriers, $\psi_i$ and $\psi_e$ are the locations of the barriers, $a_i$ and $a_e$ is the height of the barriers, $c$ is a constant to ensure $P (\psi) = 0$ at $\psi = 1$.

Figure 34: Pressure profile of double (inner and external) transport barriers given by Eq. (523) with $a_i = 1$, $b_i = 0.2$, $\psi _i = 0.36$, $\psi _e = 0.96$, $w_i = 0.2$, $w_e = 0.04$, $c = 0$.

Figure 35: Equilibrium pressure profile for EAST discharge #38300 at 3.9s (reconstructed by EFIT code, gfile name: g038300.03900), which shows a boundary transport barrier.