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## Final Model

The resulting expressions of the diffusivities are:

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

The following definitions are used:

 el_mass electron mass c velocity of light e electron charge vte_sq eletron thermal velocity squared omega_ce electron cyclotron frequency chi0 Bohm diffusitivity em_i ion atomic mass [kg]

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