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Final Model

The resulting expressions of the diffusivities are:


\begin{displaymath}\chi_{e,i}=\chi_{Be,i}+\chi_{gBe,i}\end{displaymath}

where the Bohm and gyro-Bohm terms are defined above and the adopted values of the empirical parameters are:


\begin{displaymath}\alpha_{Be} = 8\times10^{-5} ,\alpha_{Bi} = 2\times\alpha_{Be}\end{displaymath}


\begin{displaymath}\alpha_{gBe} = 3.5\times10^{-2} , \alpha_{gBi} = \alpha_{gBe}/2\end{displaymath}

The following definitions are used:

el_mass electron mass $m_e$
c velocity of light $c$
e electron charge $e$
vte_sq eletron thermal velocity squared $v_{\rm te}^2$
omega_ce electron cyclotron frequency $\omega_{\rm ce}$
chi0 Bohm diffusitivity $\chi_0$
em_i ion atomic mass [kg] $M_{\rm i}$ 

c *
c * Definition of the mixed model
c *
c
c Coefficients
c
      alfa_be  =  8.00000000000000E-05
      alfa_bi  =  1.60000000000000E-04
      alfa_gbe =  3.50000000000000E-02
      alfa_gbi =  1.75000000000000E-02
c
      coef1    =  1.00000000000000E+00
      coef2    =  3.00000000000000E-01
c
c Calculate chi0
c
      vte_sq    = tekev * zckb / zcme
      omega_ce  = zce * btor / zcme
      chi0      = vte_sq / omega_ce
c
c Calculate chibohm
c
      delta_edge = abs((te_p8 - te_edge) / te_edge)
      chi_e_bohm
     &   = abs(alfa_be * chi0 * rlpe * (q_safety**2) * delta_edge)
      chi_i_bohm
     &   = abs(alfa_bi * chi0 * rlpe * (q_safety**2) * delta_edge)
c
c Calculate chi_gyrobohm
c
      em_i      = aimass * zcmp
      v_sound   = sqrt (tekev * zckb /em_i) !                   [m/sec]
      omega_ci  = zi * zce * btor / em_i
      rho       = v_sound / omega_ci
      chi_e_gyro_bohm = abs(alfa_gbe * chi0 * gradte * rho / tekev)
      chi_i_gyro_bohm = abs(alfa_gbi * chi0 * gradte * rho / tekev)
c
c Calculate function for EXB and magnetic shear stabilization
c   use lflow = 1 for the stabilization term described by
c   T.J. Tala et al Plasma Phys. Controlled Fusion 44 (2002) A495
c
c
      vti       = sqrt (2.0 * tikev * zckb / em_i)
      gamma     = vti / (q_safety * rmaj)
c
      func = 1.0
      if ( lflow .eq. 1 ) then
        func = -0.14 + shear - 1.47 * abs(wexb*rmaj/vti)
      elseif ( lflow .eq. 2 ) then
        func = 0.1 + shear - abs (wexb / gamma)
      endif
c
      if ( func .lt. 0.0 ) then
          chi_e_bohm = 0.0
          chi_i_bohm = 0.0
      endif
c
c Now determine the actual electron and ion thermal and particle
c diffusivities.
c
      chi_e      = chi_e_bohm + chi_e_gyro_bohm
      chi_i      = chi_i_bohm + chi_i_gyro_bohm
      alfa_d    = coef1 + (coef2 - coef1) * ra
      if (abs (chi_e + chi_i) .lt. 1e-10) then
        d_hyd = 0.0
      else
        d_hyd  = abs(alfa_d * chi_e * chi_i / (chi_e + chi_i))
      endif
c
c The impurity diffusivity is not included in the mixed
c model described in Ref. [1].
c
        return
        end subroutine mixed
        end module mixed_Bohm_gyro_Bohm


transp_support 2003-10-09